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Search, Evaluate, and Read Evidence","\u002Fen\u002Facademic-writing\u002F02-reading-and-literature-matrix","en\u002Facademic-writing\u002F02-reading-and-literature-matrix",{"title":27,"path":28,"stem":29},"3. From Sources to Synthesis and Argument","\u002Fen\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs","en\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs",{"title":31,"path":32,"stem":33},"4. Literature Review and a Defensible Gap","\u002Fen\u002Facademic-writing\u002F04-writing-the-literature-review","en\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":35,"path":36,"stem":37},"5. Research Design, Evidence, and Core Sections","\u002Fen\u002Facademic-writing\u002F05-core-sections-and-evidence","en\u002Facademic-writing\u002F05-core-sections-and-evidence",{"title":39,"path":40,"stem":41},"6. Citation, Paraphrasing, Integrity, and AI","\u002Fen\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity","en\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity",{"title":43,"path":44,"stem":45},"7. Revision, Review, and Submission","\u002Fen\u002Facademic-writing\u002F07-revision-style-and-submission","en\u002Facademic-writing\u002F07-revision-style-and-submission",{"title":47,"path":48,"stem":49},"8. Research Workbook","\u002Fen\u002Facademic-writing\u002F08-literature-review-checklist-and-template","en\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":51,"path":52,"stem":53},"9. Research Workflow and Tools","\u002Fen\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management","en\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management",{"title":55,"path":56,"stem":57},"10. Worked Project — From Question to Defensible Conclusion","\u002Fen\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain","en\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain",{"title":59,"path":60,"stem":61,"children":62,"page":249},"Accounting","\u002Fen\u002Faccounting","en\u002Faccounting",[63,69,87,93,193],{"title":64,"path":65,"stem":66,"children":67},"Accounting — From Evidence to Decisions","\u002Fen\u002Faccounting\u002F00-index","en\u002Faccounting\u002F00-index",[68],{"title":64,"path":65,"stem":66},{"title":70,"path":71,"stem":72,"children":73},"Accounting Appendix","\u002Fen\u002Faccounting\u002Fappendix","en\u002Faccounting\u002Fappendix\u002Findex",[74,75,79,83],{"title":70,"path":71,"stem":72},{"title":76,"path":77,"stem":78},"Worked Examples and Error Diagnosis","\u002Fen\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls","en\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls",{"title":80,"path":81,"stem":82},"Accounting Glossary","\u002Fen\u002Faccounting\u002Fappendix\u002F26-glossary","en\u002Faccounting\u002Fappendix\u002F26-glossary",{"title":84,"path":85,"stem":86},"Reading and Evidence Map","\u002Fen\u002Faccounting\u002Fappendix\u002F27-reading-map","en\u002Faccounting\u002Fappendix\u002F27-reading-map",{"title":88,"path":89,"stem":90,"children":91},"Northstar Record-to-Decision Capstone","\u002Fen\u002Faccounting\u002Fcapstone","en\u002Faccounting\u002Fcapstone\u002Findex",[92],{"title":88,"path":89,"stem":90},{"title":94,"path":95,"stem":96,"children":97},"Financial Accounting","\u002Fen\u002Faccounting\u002Ffinancial-accounting","en\u002Faccounting\u002Ffinancial-accounting\u002Findex",[98,99,117,131,165,179],{"title":94,"path":95,"stem":96},{"title":100,"path":101,"stem":102,"children":103},"1. Foundations","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002Findex",[104,105,109,113],{"title":100,"path":101,"stem":102},{"title":106,"path":107,"stem":108},"Objectives and Qualitative Characteristics","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics",{"title":110,"path":111,"stem":112},"Equation and Elements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements",{"title":114,"path":115,"stem":116},"Accrual Basis, Estimates and Periods","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles",{"title":118,"path":119,"stem":120,"children":121},"2. Recording Transactions","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002Findex",[122,123,127],{"title":118,"path":119,"stem":120},{"title":124,"path":125,"stem":126},"Double-Entry and Debit\u002FCredit","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr",{"title":128,"path":129,"stem":130},"Accounting Cycle","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle",{"title":132,"path":133,"stem":134,"children":135},"3. Measurement and Adjustments","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002Findex",[136,137,141,145,149,153,157,161],{"title":132,"path":133,"stem":134},{"title":138,"path":139,"stem":140},"Revenue Recognition","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition",{"title":142,"path":143,"stem":144},"Inventory","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory",{"title":146,"path":147,"stem":148},"Receivables and Expected Credit Losses","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables",{"title":150,"path":151,"stem":152},"Property, Plant and Equipment","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe",{"title":154,"path":155,"stem":156},"Intangible Assets","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles",{"title":158,"path":159,"stem":160},"Leases","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases",{"title":162,"path":163,"stem":164},"Current and Deferred Income Tax","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax",{"title":166,"path":167,"stem":168,"children":169},"4. Reporting and Cash","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002Findex",[170,171,175],{"title":166,"path":167,"stem":168},{"title":172,"path":173,"stem":174},"Linked Financial Statements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements",{"title":176,"path":177,"stem":178},"Cash, Reconciliation and Internal Control","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control",{"title":180,"path":181,"stem":182,"children":183},"5. Analysis and Comparison","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002Findex",[184,185,189],{"title":180,"path":181,"stem":182},{"title":186,"path":187,"stem":188},"Ratio Analysis","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis",{"title":190,"path":191,"stem":192},"IFRS versus US GAAP","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap",{"title":194,"path":195,"stem":196,"children":197},"Management Accounting","\u002Fen\u002Faccounting\u002Fmanagement-accounting","en\u002Faccounting\u002Fmanagement-accounting\u002Findex",[198,199,217,235],{"title":194,"path":195,"stem":196},{"title":200,"path":201,"stem":202,"children":203},"1. Cost Foundations","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002Findex",[204,205,209,213],{"title":200,"path":201,"stem":202},{"title":206,"path":207,"stem":208},"Cost Concepts and Behaviour","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts",{"title":210,"path":211,"stem":212},"Costing Systems","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems",{"title":214,"path":215,"stem":216},"Variable and Absorption Costing","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption",{"title":218,"path":219,"stem":220,"children":221},"2. Planning and Control","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002Findex",[222,223,227,231],{"title":218,"path":219,"stem":220},{"title":224,"path":225,"stem":226},"Cost–Volume–Profit Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis",{"title":228,"path":229,"stem":230},"Budgeting and Variance Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances",{"title":232,"path":233,"stem":234},"Performance Measurement","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement",{"title":236,"path":237,"stem":238,"children":239},"3. Decisions and Investment","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002Findex",[240,241,245],{"title":236,"path":237,"stem":238},{"title":242,"path":243,"stem":244},"Short-Term Decisions","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions",{"title":246,"path":247,"stem":248},"Capital Budgeting","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting",false,{"title":251,"path":252,"stem":253,"children":254,"page":249},"Business Analytics","\u002Fen\u002Fbusiness-analytics","en\u002Fbusiness-analytics",[255,261,279,305,335,365,383,400],{"title":256,"path":257,"stem":258,"children":259},"Business Analytics — From Data to Defensible Action","\u002Fen\u002Fbusiness-analytics\u002F00-index","en\u002Fbusiness-analytics\u002F00-index",[260],{"title":256,"path":257,"stem":258},{"title":262,"path":263,"stem":264,"children":265},"0. Decision and Data Foundations","\u002Fen\u002Fbusiness-analytics\u002F00-intro","en\u002Fbusiness-analytics\u002F00-intro\u002Findex",[266,267,271,275],{"title":262,"path":263,"stem":264},{"title":268,"path":269,"stem":270},"Decision Framing","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing","en\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing",{"title":272,"path":273,"stem":274},"Data Contracts","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts","en\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts",{"title":276,"path":277,"stem":278},"Reproducible Analytics Workflow","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow","en\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow",{"title":280,"path":281,"stem":282,"children":283},"1. Descriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive","en\u002Fbusiness-analytics\u002F01-descriptive\u002Findex",[284,285,289,293,297,301],{"title":280,"path":281,"stem":282},{"title":286,"path":287,"stem":288},"Distributions and Exploratory Data Analysis","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda","en\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda",{"title":290,"path":291,"stem":292},"KPIs and Denominators","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators","en\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators",{"title":294,"path":295,"stem":296},"Segments, Cohorts and Funnels","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels","en\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels",{"title":298,"path":299,"stem":300},"Visual Evidence and Data Stories","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story","en\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story",{"title":302,"path":303,"stem":304},"Experiments and Causal Boundaries","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary","en\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary",{"title":306,"path":307,"stem":308,"children":309},"2. Predictive Analytics","\u002Fen\u002Fbusiness-analytics\u002F02-predictive","en\u002Fbusiness-analytics\u002F02-predictive\u002Findex",[310,311,315,319,323,327,331],{"title":306,"path":307,"stem":308},{"title":312,"path":313,"stem":314},"Validation, Baselines and Leakage","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage","en\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage",{"title":316,"path":317,"stem":318},"Regression and Forecasting","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting","en\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting",{"title":320,"path":321,"stem":322},"Classification and Calibration","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration","en\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration",{"title":324,"path":325,"stem":326},"Trees and Ensembles","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles","en\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles",{"title":328,"path":329,"stem":330},"Decision Metrics and Thresholds","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds","en\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds",{"title":332,"path":333,"stem":334},"Explainability, Monitoring and Drift","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift","en\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift",{"title":336,"path":337,"stem":338,"children":339},"3. Prescriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive","en\u002Fbusiness-analytics\u002F03-prescriptive\u002Findex",[340,341,345,349,353,357,361],{"title":336,"path":337,"stem":338},{"title":342,"path":343,"stem":344},"Decision-Making under Uncertainty","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty",{"title":346,"path":347,"stem":348},"Linear Optimisation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization",{"title":350,"path":351,"stem":352},"Inventory and Allocation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation",{"title":354,"path":355,"stem":356},"Queueing and Simulation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation",{"title":358,"path":359,"stem":360},"Pricing and Revenue Management","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation",{"title":362,"path":363,"stem":364},"Causal Targeting and Policy Learning","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting",{"title":366,"path":367,"stem":368,"children":369},"4. Deployment and Governance","\u002Fen\u002Fbusiness-analytics\u002F04-deployment","en\u002Fbusiness-analytics\u002F04-deployment\u002Findex",[370,371,375,379],{"title":366,"path":367,"stem":368},{"title":372,"path":373,"stem":374},"Data Products and Monitoring","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring","en\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring",{"title":376,"path":377,"stem":378},"Governance, Fairness and Privacy","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy","en\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy",{"title":380,"path":381,"stem":382},"Adoption and Business Value","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value","en\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value",{"title":384,"path":385,"stem":386,"children":387},"Appendix and Revision Tools","\u002Fen\u002Fbusiness-analytics\u002Fappendix","en\u002Fbusiness-analytics\u002Fappendix\u002Findex",[388,389,393,397],{"title":384,"path":385,"stem":386},{"title":390,"path":391,"stem":392},"Formula and Decision Map","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map","en\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map",{"title":394,"path":395,"stem":396},"Worked Examples and Pitfalls","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls","en\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls",{"title":84,"path":398,"stem":399},"\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map","en\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map",{"title":401,"path":402,"stem":403,"children":404},"Capstone — The Evening Delivery Promise","\u002Fen\u002Fbusiness-analytics\u002Fcapstone","en\u002Fbusiness-analytics\u002Fcapstone\u002Findex",[405],{"title":401,"path":402,"stem":403},{"title":407,"path":408,"stem":409,"children":410,"page":249},"Financial Economic Time Series","\u002Fen\u002Ffinancial-economic-time-series","en\u002Ffinancial-economic-time-series",[411,417,423,429,435,441,447,453,459,465,471],{"title":412,"path":413,"stem":414,"children":415},"Financial and Economic Time Series — Course Guide","\u002Fen\u002Ffinancial-economic-time-series\u002F00-intro","en\u002Ffinancial-economic-time-series\u002F00-intro\u002Findex",[416],{"title":412,"path":413,"stem":414},{"title":418,"path":419,"stem":420,"children":421},"Three Versions of Time Series","\u002Fen\u002Ffinancial-economic-time-series\u002F01-bridge","en\u002Ffinancial-economic-time-series\u002F01-bridge\u002Findex",[422],{"title":418,"path":419,"stem":420},{"title":424,"path":425,"stem":426,"children":427},"Data, Clocks, and Transformations","\u002Fen\u002Ffinancial-economic-time-series\u002F02-data-transformations","en\u002Ffinancial-economic-time-series\u002F02-data-transformations\u002Findex",[428],{"title":424,"path":425,"stem":426},{"title":430,"path":431,"stem":432,"children":433},"Predictive Regressions and Persistent Predictors","\u002Fen\u002Ffinancial-economic-time-series\u002F03-predictive-regressions","en\u002Ffinancial-economic-time-series\u002F03-predictive-regressions\u002Findex",[434],{"title":430,"path":431,"stem":432},{"title":436,"path":437,"stem":438,"children":439},"Volatility, Tails, and Financial Risk","\u002Fen\u002Ffinancial-economic-time-series\u002F04-volatility-risk","en\u002Ffinancial-economic-time-series\u002F04-volatility-risk\u002Findex",[440],{"title":436,"path":437,"stem":438},{"title":442,"path":443,"stem":444,"children":445},"Unit Roots, Cointegration, and Error Correction","\u002Fen\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration","en\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration\u002Findex",[446],{"title":442,"path":443,"stem":444},{"title":448,"path":449,"stem":450,"children":451},"VAR, Structural Identification, and Local Projections","\u002Fen\u002Ffinancial-economic-time-series\u002F06-var-identification","en\u002Ffinancial-economic-time-series\u002F06-var-identification\u002Findex",[452],{"title":448,"path":449,"stem":450},{"title":454,"path":455,"stem":456,"children":457},"State Space, Mixed Frequency, and Nowcasting","\u002Fen\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting","en\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting\u002Findex",[458],{"title":454,"path":455,"stem":456},{"title":460,"path":461,"stem":462,"children":463},"Forecast Evaluation for Decisions","\u002Fen\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation","en\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation\u002Findex",[464],{"title":460,"path":461,"stem":462},{"title":466,"path":467,"stem":468,"children":469},"Integrated R Laboratory","\u002Fen\u002Ffinancial-economic-time-series\u002F09-r-laboratory","en\u002Ffinancial-economic-time-series\u002F09-r-laboratory\u002Findex",[470],{"title":466,"path":467,"stem":468},{"title":472,"path":473,"stem":474,"children":475},"Capstones, Data, and Reading Ladder","\u002Fen\u002Ffinancial-economic-time-series\u002F10-capstone-readings","en\u002Ffinancial-economic-time-series\u002F10-capstone-readings\u002Findex",[476],{"title":472,"path":473,"stem":474},{"title":478,"path":479,"stem":480,"children":481,"page":249},"Intro To Economics","\u002Fen\u002Fintro-to-economics","en\u002Fintro-to-economics",[482,486,490,494,498,502,506,510,514,518,522,526,530],{"title":483,"path":484,"stem":485},"Introduction to Economics — Decisions, Markets, and the Macroeconomy","\u002Fen\u002Fintro-to-economics\u002F00-intro","en\u002Fintro-to-economics\u002F00-intro",{"title":487,"path":488,"stem":489},"Chapter 1 — Choice, Opportunity Cost, and Trade","\u002Fen\u002Fintro-to-economics\u002F01-foundations","en\u002Fintro-to-economics\u002F01-foundations",{"title":491,"path":492,"stem":493},"Chapter 2 — Demand, Supply, Equilibrium, and Welfare","\u002Fen\u002Fintro-to-economics\u002F02-demand-and-supply","en\u002Fintro-to-economics\u002F02-demand-and-supply",{"title":495,"path":496,"stem":497},"Chapter 3 — Elasticity, Revenue, and Tax Incidence","\u002Fen\u002Fintro-to-economics\u002F03-elasticity","en\u002Fintro-to-economics\u002F03-elasticity",{"title":499,"path":500,"stem":501},"Chapter 4 — Firms, Market Power, and Market Failure","\u002Fen\u002Fintro-to-economics\u002F04-market-structures","en\u002Fintro-to-economics\u002F04-market-structures",{"title":503,"path":504,"stem":505},"Chapter 5 — GDP, Income, Wealth, and Welfare","\u002Fen\u002Fintro-to-economics\u002F05-gdp-and-wealth","en\u002Fintro-to-economics\u002F05-gdp-and-wealth",{"title":507,"path":508,"stem":509},"Chapter 6 — Inflation, Purchasing Power, and Labour Markets","\u002Fen\u002Fintro-to-economics\u002F06-inflation-and-unemployment","en\u002Fintro-to-economics\u002F06-inflation-and-unemployment",{"title":511,"path":512,"stem":513},"Chapter 7 — Productivity, Technology, and Economic Growth","\u002Fen\u002Fintro-to-economics\u002F07-economic-growth","en\u002Fintro-to-economics\u002F07-economic-growth",{"title":515,"path":516,"stem":517},"Chapter 8 — Money, Credit, and Banking","\u002Fen\u002Fintro-to-economics\u002F08-money-and-banking","en\u002Fintro-to-economics\u002F08-money-and-banking",{"title":519,"path":520,"stem":521},"Chapter 9 — Business Cycles, AD–AS, and Monetary Policy","\u002Fen\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as","en\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as",{"title":523,"path":524,"stem":525},"Chapter 10 — Fiscal Policy, Distribution, and Public Debt","\u002Fen\u002Fintro-to-economics\u002F10-fiscal-policy","en\u002Fintro-to-economics\u002F10-fiscal-policy",{"title":527,"path":528,"stem":529},"Chapter 11 — Trade, Capital Flows, and Exchange Rates","\u002Fen\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates","en\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates",{"title":531,"path":532,"stem":533},"Chapter 12 — Integrated Economic Analysis Studio","\u002Fen\u002Fintro-to-economics\u002F12-review-and-case-studies","en\u002Fintro-to-economics\u002F12-review-and-case-studies",{"title":535,"path":536,"stem":537,"children":538,"page":249},"Microeconometrics","\u002Fen\u002Fmicroeconometrics","en\u002Fmicroeconometrics",[539,557,563,581,603,629,651,673,691,709],{"title":540,"path":541,"stem":542,"children":543},"0. Causal Questions and Designs","\u002Fen\u002Fmicroeconometrics\u002F00-foundations","en\u002Fmicroeconometrics\u002F00-foundations\u002Findex",[544,545,549,553],{"title":540,"path":541,"stem":542},{"title":546,"path":547,"stem":548},"Causal Questions and Estimands","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands","en\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands",{"title":550,"path":551,"stem":552},"Potential Outcomes and Experiments","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments","en\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments",{"title":554,"path":555,"stem":556},"Causal Diagrams and Controls","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls","en\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls",{"title":558,"path":559,"stem":560,"children":561},"Microeconometrics — Designing Credible Counterfactuals","\u002Fen\u002Fmicroeconometrics\u002F00-index","en\u002Fmicroeconometrics\u002F00-index",[562],{"title":558,"path":559,"stem":560},{"title":564,"path":565,"stem":566,"children":567},"1. Regression and Inference","\u002Fen\u002Fmicroeconometrics\u002F01-regression","en\u002Fmicroeconometrics\u002F01-regression\u002Findex",[568,569,573,577],{"title":564,"path":565,"stem":566},{"title":570,"path":571,"stem":572},"OLS as a Projection","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection","en\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection",{"title":574,"path":575,"stem":576},"FWL, Selection and Controls","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls","en\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls",{"title":578,"path":579,"stem":580},"Inference and Clustering","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering","en\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering",{"title":582,"path":583,"stem":584,"children":585},"2. Instruments and Panel Data","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002Findex",[586,587,591,595,599],{"title":582,"path":583,"stem":584},{"title":588,"path":589,"stem":590},"Instrumental Variables","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification",{"title":592,"path":593,"stem":594},"Weak Instruments and LATE","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late",{"title":596,"path":597,"stem":598},"Panel Fixed Effects","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects",{"title":600,"path":601,"stem":602},"Dynamic Panels and Limits","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel",{"title":604,"path":605,"stem":606,"children":607},"3. Policy Evaluation Designs","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs","en\u002Fmicroeconometrics\u002F03-policy-designs\u002Findex",[608,609,613,617,621,625],{"title":604,"path":605,"stem":606},{"title":610,"path":611,"stem":612},"Difference-in-Differences","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core",{"title":614,"path":615,"stem":616},"Staggered DID and Event Studies","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies",{"title":618,"path":619,"stem":620},"Regression Discontinuity","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd",{"title":622,"path":623,"stem":624},"Matching, Weighting and Overlap","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting",{"title":626,"path":627,"stem":628},"Synthetic Control","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control",{"title":630,"path":631,"stem":632,"children":633},"Module 4 — Choice and Limited Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002Findex",[634,635,639,643,647],{"title":630,"path":631,"stem":632},{"title":636,"path":637,"stem":638},"Binary Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice",{"title":640,"path":641,"stem":642},"Multinomial and Ordered Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice",{"title":644,"path":645,"stem":646},"Count Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes",{"title":648,"path":649,"stem":650},"Censoring, Truncation and Selection","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection",{"title":652,"path":653,"stem":654,"children":655},"Module 5 — Modern Causal Analysis","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal","en\u002Fmicroeconometrics\u002F05-modern-causal\u002Findex",[656,657,661,665,669],{"title":652,"path":653,"stem":654},{"title":658,"path":659,"stem":660},"Double Machine Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml",{"title":662,"path":663,"stem":664},"Heterogeneity and Policy Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy",{"title":666,"path":667,"stem":668},"Sensitivity and Partial Identification","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id",{"title":670,"path":671,"stem":672},"External Validity and Transport","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity",{"title":674,"path":675,"stem":676,"children":677},"Module 6 — From Data to Auditable Evidence","\u002Fen\u002Fmicroeconometrics\u002F06-workflow","en\u002Fmicroeconometrics\u002F06-workflow\u002Findex",[678,679,683,687],{"title":674,"path":675,"stem":676},{"title":680,"path":681,"stem":682},"Data Provenance","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance","en\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance",{"title":684,"path":685,"stem":686},"Reproducibility and Reporting","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting","en\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting",{"title":688,"path":689,"stem":690},"Paper and Evidence Audit","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit","en\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit",{"title":692,"path":693,"stem":694,"children":695},"Appendix — Revision and Evidence Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix","en\u002Fmicroeconometrics\u002Fappendix\u002Findex",[696,697,701,705],{"title":692,"path":693,"stem":694},{"title":698,"path":699,"stem":700},"Formula and Design Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map","en\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map",{"title":702,"path":703,"stem":704},"Ten Worked Microeconometric Pitfalls","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls","en\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls",{"title":706,"path":707,"stem":708},"Reading and Software Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map","en\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map",{"title":710,"path":711,"stem":712,"children":713},"Capstone — Should Northbridge Expand Pathways?","\u002Fen\u002Fmicroeconometrics\u002Fcapstone","en\u002Fmicroeconometrics\u002Fcapstone\u002Findex",[714],{"title":710,"path":711,"stem":712},{"title":716,"path":717,"stem":718,"children":719,"page":249},"Microeconomics","\u002Fen\u002Fmicroeconomics","en\u002Fmicroeconomics",[720,726,732,738,744,750,756,762,768,774,780,786,792],{"title":721,"path":722,"stem":723,"children":724},"Advanced Microeconomics — Course Guide","\u002Fen\u002Fmicroeconomics\u002F00-intro","en\u002Fmicroeconomics\u002F00-intro\u002Findex",[725],{"title":721,"path":722,"stem":723},{"title":727,"path":728,"stem":729,"children":730},"Module 1 — Choice, Duality, and Revealed Preference","\u002Fen\u002Fmicroeconomics\u002F01-fundations","en\u002Fmicroeconomics\u002F01-fundations\u002Findex",[731],{"title":727,"path":728,"stem":729},{"title":733,"path":734,"stem":735,"children":736},"Module 2 — Comparative Statics and Welfare Measurement","\u002Fen\u002Fmicroeconomics\u002F02-comparative-statics","en\u002Fmicroeconomics\u002F02-comparative-statics\u002Findex",[737],{"title":733,"path":734,"stem":735},{"title":739,"path":740,"stem":741,"children":742},"Module 3 — Choice under Risk and Insurance","\u002Fen\u002Fmicroeconomics\u002F03-uncertainty","en\u002Fmicroeconomics\u002F03-uncertainty\u002Findex",[743],{"title":739,"path":740,"stem":741},{"title":745,"path":746,"stem":747,"children":748},"Module 4 — General Equilibrium and Welfare","\u002Fen\u002Fmicroeconomics\u002F04-general-equilibrium","en\u002Fmicroeconomics\u002F04-general-equilibrium\u002Findex",[749],{"title":745,"path":746,"stem":747},{"title":751,"path":752,"stem":753,"children":754},"Module 5 — Static, Dynamic, and Repeated Games","\u002Fen\u002Fmicroeconomics\u002F05-game-theory","en\u002Fmicroeconomics\u002F05-game-theory\u002Findex",[755],{"title":751,"path":752,"stem":753},{"title":757,"path":758,"stem":759,"children":760},"Module 6 — Oligopoly, Entry, and Algorithmic Pricing","\u002Fen\u002Fmicroeconomics\u002F06-oligopoly","en\u002Fmicroeconomics\u002F06-oligopoly\u002Findex",[761],{"title":757,"path":758,"stem":759},{"title":763,"path":764,"stem":765,"children":766},"Module 7 — Information Economics and Contracts","\u002Fen\u002Fmicroeconomics\u002F07-information-economics","en\u002Fmicroeconomics\u002F07-information-economics\u002Findex",[767],{"title":763,"path":764,"stem":765},{"title":769,"path":770,"stem":771,"children":772},"Module 8 — Mechanism Design and Auctions","\u002Fen\u002Fmicroeconomics\u002F08-mechanism-design","en\u002Fmicroeconomics\u002F08-mechanism-design\u002Findex",[773],{"title":769,"path":770,"stem":771},{"title":775,"path":776,"stem":777,"children":778},"Module 9 — Behavioural and Experimental Microeconomics","\u002Fen\u002Fmicroeconomics\u002F09-behavioural-economics","en\u002Fmicroeconomics\u002F09-behavioural-economics\u002Findex",[779],{"title":775,"path":776,"stem":777},{"title":781,"path":782,"stem":783,"children":784},"Module 10 — Externalities, Public Goods, and Collective Action","\u002Fen\u002Fmicroeconomics\u002F10-externalities-public-goods","en\u002Fmicroeconomics\u002F10-externalities-public-goods\u002Findex",[785],{"title":781,"path":782,"stem":783},{"title":787,"path":788,"stem":789,"children":790},"Module 11 — Matching and Market Design","\u002Fen\u002Fmicroeconomics\u002F11-market-design","en\u002Fmicroeconomics\u002F11-market-design\u002Findex",[791],{"title":787,"path":788,"stem":789},{"title":793,"path":794,"stem":795,"children":796},"Module 12 — Integrated Microeconomic Design Studio","\u002Fen\u002Fmicroeconomics\u002F12-review","en\u002Fmicroeconomics\u002F12-review\u002Findex",[797],{"title":793,"path":794,"stem":795},{"title":799,"path":800,"stem":801,"children":802},"Playground","\u002Fen\u002Fplayground","en\u002Fplayground\u002Findex",[803,804,808,812,816,820],{"title":799,"path":800,"stem":801},{"title":805,"path":806,"stem":807},"Typst Plugin Playground","\u002Fen\u002Fplayground\u002F01-typstex","en\u002Fplayground\u002F01-typstex",{"title":809,"path":810,"stem":811},"Citation Plugin Test","\u002Fen\u002Fplayground\u002F02-citation","en\u002Fplayground\u002F02-citation",{"title":813,"path":814,"stem":815},"Pyodide Playground","\u002Fen\u002Fplayground\u002F03-pyodide","en\u002Fplayground\u002F03-pyodide",{"title":817,"path":818,"stem":819},"WebR Playground","\u002Fen\u002Fplayground\u002F04-webr","en\u002Fplayground\u002F04-webr",{"title":821,"path":822,"stem":823},"Chart.js 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文献综述的构建与写作","\u002Fzh\u002Facademic-writing\u002F04-writing-the-literature-review","zh\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":1056,"path":1057,"stem":1058},"8. 文献综述清单与模板","\u002Fzh\u002Facademic-writing\u002F08-literature-review-checklist-and-template","zh\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":1060,"path":1061,"stem":1062},"10. 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Alpha 策略全流程","\u002Fzh\u002Fquant\u002F09-case-study","zh\u002Fquant\u002F09-case-study",{"title":1779,"path":1780,"stem":1781},"量化投资文献与软件图谱","\u002Fzh\u002Fquant\u002F10-reading-software-map","zh\u002Fquant\u002F10-reading-software-map",null,{"id":1784,"title":1651,"body":1785,"description":5222,"extension":5223,"features":1782,"hero":1782,"layout":1782,"locale":1782,"meta":5224,"navigation":1782,"path":1652,"published":5226,"seo":5227,"stem":1653,"__hash__":5228},"docs\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F01-prob-theory\u002Findex.md",{"type":1786,"value":1787,"toc":5208},"minimark",[1788,1792,1803,1806,1810,1813,1832,1836,1947,2579,2582,2731,2943,3034,3038,3312,3315,3468,3605,3609,3800,3904,3907,3911,4058,4361,4364,4921,4924,4928,4931,4938,4941,4945,4948,4952,4955,4959,4986,4990,5142,5145,5148,5162,5165,5195],[1789,1790,1651],"h1",{"id":1791},"第一章概率论基础",[1793,1794,1795],"blockquote",{},[1796,1797,1798,1802],"p",{},[1799,1800,1801],"strong",{},"案例："," 一项检测灵敏度 95%、特异度 90%。检测阳性的人真正患病概率是 95% 吗？",[1796,1804,1805],{},"概率不是直觉强弱，而是在清楚样本空间与信息条件下，对事件不确定性的量化。",[1807,1808,1809],"h2",{"id":1809},"学习目标",[1796,1811,1812],{},"你应能：",[1814,1815,1816,1820,1823,1826,1829],"ol",{},[1817,1818,1819],"li",{},"定义样本空间、事件与概率；",[1817,1821,1822],{},"使用补集、加法公式和计数法；",[1817,1824,1825],{},"区分条件概率与独立性；",[1817,1827,1828],{},"用全概率公式拆分路径；",[1817,1830,1831],{},"用贝叶斯公式更新概率并解释基准率。",[1807,1833,1835],{"id":1834},"_1-样本空间先于公式","1. 样本空间先于公式",[1796,1837,1838,1839,1886,1887,1946],{},"随机试验所有可能基本结果组成样本空间 ",[1840,1841,1844,1868],"span",{"className":1842},[1843],"katex",[1840,1845,1848],{"className":1846},[1847],"katex-mathml",[1849,1850,1852],"math",{"xmlns":1851},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1853,1854,1855,1863],"semantics",{},[1856,1857,1858],"mrow",{},[1859,1860,1862],"mi",{"mathvariant":1861},"normal","Ω",[1864,1865,1867],"annotation",{"encoding":1866},"application\u002Fx-tex","\\Omega",[1840,1869,1873],{"className":1870,"ariaHidden":1872},[1871],"katex-html","true",[1840,1874,1877,1882],{"className":1875},[1876],"base",[1840,1878],{"className":1879,"style":1881},[1880],"strut","height:0.6833em;",[1840,1883,1862],{"className":1884},[1885],"mord","，事件 ",[1840,1888,1890,1911],{"className":1889},[1843],[1840,1891,1893],{"className":1892},[1847],[1849,1894,1895],{"xmlns":1851},[1853,1896,1897,1908],{},[1856,1898,1899,1902,1906],{},[1859,1900,1901],{},"A",[1903,1904,1905],"mo",{},"⊆",[1859,1907,1862],{"mathvariant":1861},[1864,1909,1910],{"encoding":1866},"A\\subseteq\\Omega",[1840,1912,1914,1937],{"className":1913,"ariaHidden":1872},[1871],[1840,1915,1917,1921,1925,1930,1934],{"className":1916},[1876],[1840,1918],{"className":1919,"style":1920},[1880],"height:0.8193em;vertical-align:-0.136em;",[1840,1922,1901],{"className":1923},[1885,1924],"mathnormal",[1840,1926],{"className":1927,"style":1929},[1928],"mspace","margin-right:0.2778em;",[1840,1931,1905],{"className":1932},[1933],"mrel",[1840,1935],{"className":1936,"style":1929},[1928],[1840,1938,1940,1943],{"className":1939},[1876],[1840,1941],{"className":1942,"style":1881},[1880],[1840,1944,1862],{"className":1945},[1885],"。概率测度满足：",[1814,1948,1949,2030,2100],{},[1817,1950,1951,2029],{},[1840,1952,1954,1985],{"className":1953},[1843],[1840,1955,1957],{"className":1956},[1847],[1849,1958,1959],{"xmlns":1851},[1853,1960,1961,1982],{},[1856,1962,1963,1966,1970,1972,1975,1978],{},[1859,1964,1965],{},"P",[1903,1967,1969],{"stretchy":1968},"false","(",[1859,1971,1901],{},[1903,1973,1974],{"stretchy":1968},")",[1903,1976,1977],{},"≥",[1979,1980,1981],"mn",{},"0",[1864,1983,1984],{"encoding":1866},"P(A)\\ge0",[1840,1986,1988,2019],{"className":1987,"ariaHidden":1872},[1871],[1840,1989,1991,1995,1999,2003,2006,2010,2013,2016],{"className":1990},[1876],[1840,1992],{"className":1993,"style":1994},[1880],"height:1em;vertical-align:-0.25em;",[1840,1996,1965],{"className":1997,"style":1998},[1885,1924],"margin-right:0.1389em;",[1840,2000,1969],{"className":2001},[2002],"mopen",[1840,2004,1901],{"className":2005},[1885,1924],[1840,2007,1974],{"className":2008},[2009],"mclose",[1840,2011],{"className":2012,"style":1929},[1928],[1840,2014,1977],{"className":2015},[1933],[1840,2017],{"className":2018,"style":1929},[1928],[1840,2020,2022,2026],{"className":2021},[1876],[1840,2023],{"className":2024,"style":2025},[1880],"height:0.6444em;",[1840,2027,1981],{"className":2028},[1885],"；",[1817,2031,2032,2029],{},[1840,2033,2035,2061],{"className":2034},[1843],[1840,2036,2038],{"className":2037},[1847],[1849,2039,2040],{"xmlns":1851},[1853,2041,2042,2058],{},[1856,2043,2044,2046,2048,2050,2052,2055],{},[1859,2045,1965],{},[1903,2047,1969],{"stretchy":1968},[1859,2049,1862],{"mathvariant":1861},[1903,2051,1974],{"stretchy":1968},[1903,2053,2054],{},"=",[1979,2056,2057],{},"1",[1864,2059,2060],{"encoding":1866},"P(\\Omega)=1",[1840,2062,2064,2091],{"className":2063,"ariaHidden":1872},[1871],[1840,2065,2067,2070,2073,2076,2079,2082,2085,2088],{"className":2066},[1876],[1840,2068],{"className":2069,"style":1994},[1880],[1840,2071,1965],{"className":2072,"style":1998},[1885,1924],[1840,2074,1969],{"className":2075},[2002],[1840,2077,1862],{"className":2078},[1885],[1840,2080,1974],{"className":2081},[2009],[1840,2083],{"className":2084,"style":1929},[1928],[1840,2086,2054],{"className":2087},[1933],[1840,2089],{"className":2090,"style":1929},[1928],[1840,2092,2094,2097],{"className":2093},[1876],[1840,2095],{"className":2096,"style":2025},[1880],[1840,2098,2057],{"className":2099},[1885],[1817,2101,2102,2103,2264,2265],{},"对两两互斥的 ",[1840,2104,2106,2140],{"className":2105},[1843],[1840,2107,2109],{"className":2108},[1847],[1849,2110,2111],{"xmlns":1851},[1853,2112,2113,2137],{},[1856,2114,2115,2122,2125,2132,2134],{},[2116,2117,2118,2120],"msub",{},[1859,2119,1901],{},[1979,2121,2057],{},[1903,2123,2124],{"separator":1872},",",[2116,2126,2127,2129],{},[1859,2128,1901],{},[1979,2130,2131],{},"2",[1903,2133,2124],{"separator":1872},[1903,2135,2136],{},"…",[1864,2138,2139],{"encoding":1866},"A_1,A_2,\\ldots",[1840,2141,2143],{"className":2142,"ariaHidden":1872},[1871],[1840,2144,2146,2150,2206,2210,2214,2254,2257,2260],{"className":2145},[1876],[1840,2147],{"className":2148,"style":2149},[1880],"height:0.8778em;vertical-align:-0.1944em;",[1840,2151,2153,2156],{"className":2152},[1885],[1840,2154,1901],{"className":2155},[1885,1924],[1840,2157,2160],{"className":2158},[2159],"msupsub",[1840,2161,2165,2197],{"className":2162},[2163,2164],"vlist-t","vlist-t2",[1840,2166,2169,2192],{"className":2167},[2168],"vlist-r",[1840,2170,2174],{"className":2171,"style":2173},[2172],"vlist","height:0.3011em;",[1840,2175,2177,2182],{"style":2176},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1840,2178],{"className":2179,"style":2181},[2180],"pstrut","height:2.7em;",[1840,2183,2189],{"className":2184},[2185,2186,2187,2188],"sizing","reset-size6","size3","mtight",[1840,2190,2057],{"className":2191},[1885,2188],[1840,2193,2196],{"className":2194},[2195],"vlist-s","​",[1840,2198,2200],{"className":2199},[2168],[1840,2201,2204],{"className":2202,"style":2203},[2172],"height:0.15em;",[1840,2205],{},[1840,2207,2124],{"className":2208},[2209],"mpunct",[1840,2211],{"className":2212,"style":2213},[1928],"margin-right:0.1667em;",[1840,2215,2217,2220],{"className":2216},[1885],[1840,2218,1901],{"className":2219},[1885,1924],[1840,2221,2223],{"className":2222},[2159],[1840,2224,2226,2246],{"className":2225},[2163,2164],[1840,2227,2229,2243],{"className":2228},[2168],[1840,2230,2232],{"className":2231,"style":2173},[2172],[1840,2233,2234,2237],{"style":2176},[1840,2235],{"className":2236,"style":2181},[2180],[1840,2238,2240],{"className":2239},[2185,2186,2187,2188],[1840,2241,2131],{"className":2242},[1885,2188],[1840,2244,2196],{"className":2245},[2195],[1840,2247,2249],{"className":2248},[2168],[1840,2250,2252],{"className":2251,"style":2203},[2172],[1840,2253],{},[1840,2255,2124],{"className":2256},[2209],[1840,2258],{"className":2259,"style":2213},[1928],[1840,2261,2136],{"className":2262},[2263],"minner","，",[1840,2266,2269],{"className":2267},[2268],"katex-display",[1840,2270,2272,2332],{"className":2271},[1843],[1840,2273,2275],{"className":2274},[1847],[1849,2276,2278],{"xmlns":1851,"display":2277},"block",[1853,2279,2280,2329],{},[1856,2281,2282,2284,2305,2307,2314,2316,2318,2324,2326],{},[1859,2283,1965],{},[1856,2285,2286,2288,2297,2303],{},[1903,2287,1969],{"fence":1872},[2289,2290,2291,2294],"munder",{},[1903,2292,2293],{},"⋃",[1859,2295,2296],{},"i",[2116,2298,2299,2301],{},[1859,2300,1901],{},[1859,2302,2296],{},[1903,2304,1974],{"fence":1872},[1903,2306,2054],{},[2289,2308,2309,2312],{},[1903,2310,2311],{},"∑",[1859,2313,2296],{},[1859,2315,1965],{},[1903,2317,1969],{"stretchy":1968},[2116,2319,2320,2322],{},[1859,2321,1901],{},[1859,2323,2296],{},[1903,2325,1974],{"stretchy":1968},[1859,2327,2328],{"mathvariant":1861},".",[1864,2330,2331],{"encoding":1866},"P\\left(\\bigcup_iA_i\\right)=\\sum_iP(A_i).",[1840,2333,2335,2473],{"className":2334,"ariaHidden":1872},[1871],[1840,2336,2338,2342,2345,2348,2464,2467,2470],{"className":2337},[1876],[1840,2339],{"className":2340,"style":2341},[1880],"height:3.0277em;vertical-align:-1.2777em;",[1840,2343,1965],{"className":2344,"style":1998},[1885,1924],[1840,2346],{"className":2347,"style":2213},[1928],[1840,2349,2351,2361,2414,2417,2458],{"className":2350},[2263],[1840,2352,2356],{"className":2353,"style":2355},[2002,2354],"delimcenter","top:0em;",[1840,2357,1969],{"className":2358},[2359,2360],"delimsizing","size4",[1840,2362,2366],{"className":2363},[2364,2365],"mop","op-limits",[1840,2367,2369,2405],{"className":2368},[2163,2164],[1840,2370,2372,2402],{"className":2371},[2168],[1840,2373,2376,2389],{"className":2374,"style":2375},[2172],"height:1.05em;",[1840,2377,2379,2383],{"style":2378},"top:-1.8723em;margin-left:0em;",[1840,2380],{"className":2381,"style":2382},[2180],"height:3.05em;",[1840,2384,2386],{"className":2385},[2185,2186,2187,2188],[1840,2387,2296],{"className":2388},[1885,1924,2188],[1840,2390,2392,2395],{"style":2391},"top:-3.05em;",[1840,2393],{"className":2394,"style":2382},[2180],[1840,2396,2397],{},[1840,2398,2293],{"className":2399},[2364,2400,2401],"op-symbol","large-op",[1840,2403,2196],{"className":2404},[2195],[1840,2406,2408],{"className":2407},[2168],[1840,2409,2412],{"className":2410,"style":2411},[2172],"height:1.2777em;",[1840,2413],{},[1840,2415],{"className":2416,"style":2213},[1928],[1840,2418,2420,2423],{"className":2419},[1885],[1840,2421,1901],{"className":2422},[1885,1924],[1840,2424,2426],{"className":2425},[2159],[1840,2427,2429,2450],{"className":2428},[2163,2164],[1840,2430,2432,2447],{"className":2431},[2168],[1840,2433,2436],{"className":2434,"style":2435},[2172],"height:0.3117em;",[1840,2437,2438,2441],{"style":2176},[1840,2439],{"className":2440,"style":2181},[2180],[1840,2442,2444],{"className":2443},[2185,2186,2187,2188],[1840,2445,2296],{"className":2446},[1885,1924,2188],[1840,2448,2196],{"className":2449},[2195],[1840,2451,2453],{"className":2452},[2168],[1840,2454,2456],{"className":2455,"style":2203},[2172],[1840,2457],{},[1840,2459,2461],{"className":2460,"style":2355},[2009,2354],[1840,2462,1974],{"className":2463},[2359,2360],[1840,2465],{"className":2466,"style":1929},[1928],[1840,2468,2054],{"className":2469},[1933],[1840,2471],{"className":2472,"style":1929},[1928],[1840,2474,2476,2480,2524,2527,2530,2533,2573,2576],{"className":2475},[1876],[1840,2477],{"className":2478,"style":2479},[1880],"height:2.3277em;vertical-align:-1.2777em;",[1840,2481,2483],{"className":2482},[2364,2365],[1840,2484,2486,2516],{"className":2485},[2163,2164],[1840,2487,2489,2513],{"className":2488},[2168],[1840,2490,2492,2503],{"className":2491,"style":2375},[2172],[1840,2493,2494,2497],{"style":2378},[1840,2495],{"className":2496,"style":2382},[2180],[1840,2498,2500],{"className":2499},[2185,2186,2187,2188],[1840,2501,2296],{"className":2502},[1885,1924,2188],[1840,2504,2505,2508],{"style":2391},[1840,2506],{"className":2507,"style":2382},[2180],[1840,2509,2510],{},[1840,2511,2311],{"className":2512},[2364,2400,2401],[1840,2514,2196],{"className":2515},[2195],[1840,2517,2519],{"className":2518},[2168],[1840,2520,2522],{"className":2521,"style":2411},[2172],[1840,2523],{},[1840,2525],{"className":2526,"style":2213},[1928],[1840,2528,1965],{"className":2529,"style":1998},[1885,1924],[1840,2531,1969],{"className":2532},[2002],[1840,2534,2536,2539],{"className":2535},[1885],[1840,2537,1901],{"className":2538},[1885,1924],[1840,2540,2542],{"className":2541},[2159],[1840,2543,2545,2565],{"className":2544},[2163,2164],[1840,2546,2548,2562],{"className":2547},[2168],[1840,2549,2551],{"className":2550,"style":2435},[2172],[1840,2552,2553,2556],{"style":2176},[1840,2554],{"className":2555,"style":2181},[2180],[1840,2557,2559],{"className":2558},[2185,2186,2187,2188],[1840,2560,2296],{"className":2561},[1885,1924,2188],[1840,2563,2196],{"className":2564},[2195],[1840,2566,2568],{"className":2567},[2168],[1840,2569,2571],{"className":2570,"style":2203},[2172],[1840,2572],{},[1840,2574,1974],{"className":2575},[2009],[1840,2577,2328],{"className":2578},[1885],[1796,2580,2581],{},"立即得到：",[1840,2583,2585],{"className":2584},[2268],[1840,2586,2588,2631],{"className":2587},[1843],[1840,2589,2591],{"className":2590},[1847],[1849,2592,2593],{"xmlns":1851,"display":2277},[1853,2594,2595,2628],{},[1856,2596,2597,2599,2601,2609,2611,2613,2615,2618,2620,2622,2624,2626],{},[1859,2598,1965],{},[1903,2600,1969],{"stretchy":1968},[2602,2603,2604,2606],"msup",{},[1859,2605,1901],{},[1859,2607,2608],{},"c",[1903,2610,1974],{"stretchy":1968},[1903,2612,2054],{},[1979,2614,2057],{},[1903,2616,2617],{},"−",[1859,2619,1965],{},[1903,2621,1969],{"stretchy":1968},[1859,2623,1901],{},[1903,2625,1974],{"stretchy":1968},[1903,2627,2124],{"separator":1872},[1864,2629,2630],{"encoding":1866},"P(A^c)=1-P(A),",[1840,2632,2634,2689,2710],{"className":2633,"ariaHidden":1872},[1871],[1840,2635,2637,2640,2643,2646,2677,2680,2683,2686],{"className":2636},[1876],[1840,2638],{"className":2639,"style":1994},[1880],[1840,2641,1965],{"className":2642,"style":1998},[1885,1924],[1840,2644,1969],{"className":2645},[2002],[1840,2647,2649,2652],{"className":2648},[1885],[1840,2650,1901],{"className":2651},[1885,1924],[1840,2653,2655],{"className":2654},[2159],[1840,2656,2658],{"className":2657},[2163],[1840,2659,2661],{"className":2660},[2168],[1840,2662,2665],{"className":2663,"style":2664},[2172],"height:0.7144em;",[1840,2666,2668,2671],{"style":2667},"top:-3.113em;margin-right:0.05em;",[1840,2669],{"className":2670,"style":2181},[2180],[1840,2672,2674],{"className":2673},[2185,2186,2187,2188],[1840,2675,2608],{"className":2676},[1885,1924,2188],[1840,2678,1974],{"className":2679},[2009],[1840,2681],{"className":2682,"style":1929},[1928],[1840,2684,2054],{"className":2685},[1933],[1840,2687],{"className":2688,"style":1929},[1928],[1840,2690,2692,2696,2699,2703,2707],{"className":2691},[1876],[1840,2693],{"className":2694,"style":2695},[1880],"height:0.7278em;vertical-align:-0.0833em;",[1840,2697,2057],{"className":2698},[1885],[1840,2700],{"className":2701,"style":2702},[1928],"margin-right:0.2222em;",[1840,2704,2617],{"className":2705},[2706],"mbin",[1840,2708],{"className":2709,"style":2702},[1928],[1840,2711,2713,2716,2719,2722,2725,2728],{"className":2712},[1876],[1840,2714],{"className":2715,"style":1994},[1880],[1840,2717,1965],{"className":2718,"style":1998},[1885,1924],[1840,2720,1969],{"className":2721},[2002],[1840,2723,1901],{"className":2724},[1885,1924],[1840,2726,1974],{"className":2727},[2009],[1840,2729,2124],{"className":2730},[2209],[1840,2732,2734],{"className":2733},[2268],[1840,2735,2737,2801],{"className":2736},[1843],[1840,2738,2740],{"className":2739},[1847],[1849,2741,2742],{"xmlns":1851,"display":2277},[1853,2743,2744,2798],{},[1856,2745,2746,2748,2750,2752,2755,2758,2760,2762,2764,2766,2768,2770,2773,2775,2777,2779,2781,2783,2785,2787,2789,2792,2794,2796],{},[1859,2747,1965],{},[1903,2749,1969],{"stretchy":1968},[1859,2751,1901],{},[1903,2753,2754],{},"∪",[1859,2756,2757],{},"B",[1903,2759,1974],{"stretchy":1968},[1903,2761,2054],{},[1859,2763,1965],{},[1903,2765,1969],{"stretchy":1968},[1859,2767,1901],{},[1903,2769,1974],{"stretchy":1968},[1903,2771,2772],{},"+",[1859,2774,1965],{},[1903,2776,1969],{"stretchy":1968},[1859,2778,2757],{},[1903,2780,1974],{"stretchy":1968},[1903,2782,2617],{},[1859,2784,1965],{},[1903,2786,1969],{"stretchy":1968},[1859,2788,1901],{},[1903,2790,2791],{},"∩",[1859,2793,2757],{},[1903,2795,1974],{"stretchy":1968},[1859,2797,2328],{"mathvariant":1861},[1864,2799,2800],{"encoding":1866},"P(A\\cup B)=P(A)+P(B)-P(A\\cap B).",[1840,2802,2804,2828,2850,2877,2904,2928],{"className":2803,"ariaHidden":1872},[1871],[1840,2805,2807,2810,2813,2816,2819,2822,2825],{"className":2806},[1876],[1840,2808],{"className":2809,"style":1994},[1880],[1840,2811,1965],{"className":2812,"style":1998},[1885,1924],[1840,2814,1969],{"className":2815},[2002],[1840,2817,1901],{"className":2818},[1885,1924],[1840,2820],{"className":2821,"style":2702},[1928],[1840,2823,2754],{"className":2824},[2706],[1840,2826],{"className":2827,"style":2702},[1928],[1840,2829,2831,2834,2838,2841,2844,2847],{"className":2830},[1876],[1840,2832],{"className":2833,"style":1994},[1880],[1840,2835,2757],{"className":2836,"style":2837},[1885,1924],"margin-right:0.0502em;",[1840,2839,1974],{"className":2840},[2009],[1840,2842],{"className":2843,"style":1929},[1928],[1840,2845,2054],{"className":2846},[1933],[1840,2848],{"className":2849,"style":1929},[1928],[1840,2851,2853,2856,2859,2862,2865,2868,2871,2874],{"className":2852},[1876],[1840,2854],{"className":2855,"style":1994},[1880],[1840,2857,1965],{"className":2858,"style":1998},[1885,1924],[1840,2860,1969],{"className":2861},[2002],[1840,2863,1901],{"className":2864},[1885,1924],[1840,2866,1974],{"className":2867},[2009],[1840,2869],{"className":2870,"style":2702},[1928],[1840,2872,2772],{"className":2873},[2706],[1840,2875],{"className":2876,"style":2702},[1928],[1840,2878,2880,2883,2886,2889,2892,2895,2898,2901],{"className":2879},[1876],[1840,2881],{"className":2882,"style":1994},[1880],[1840,2884,1965],{"className":2885,"style":1998},[1885,1924],[1840,2887,1969],{"className":2888},[2002],[1840,2890,2757],{"className":2891,"style":2837},[1885,1924],[1840,2893,1974],{"className":2894},[2009],[1840,2896],{"className":2897,"style":2702},[1928],[1840,2899,2617],{"className":2900},[2706],[1840,2902],{"className":2903,"style":2702},[1928],[1840,2905,2907,2910,2913,2916,2919,2922,2925],{"className":2906},[1876],[1840,2908],{"className":2909,"style":1994},[1880],[1840,2911,1965],{"className":2912,"style":1998},[1885,1924],[1840,2914,1969],{"className":2915},[2002],[1840,2917,1901],{"className":2918},[1885,1924],[1840,2920],{"className":2921,"style":2702},[1928],[1840,2923,2791],{"className":2924},[2706],[1840,2926],{"className":2927,"style":2702},[1928],[1840,2929,2931,2934,2937,2940],{"className":2930},[1876],[1840,2932],{"className":2933,"style":1994},[1880],[1840,2935,2757],{"className":2936,"style":2837},[1885,1924],[1840,2938,1974],{"className":2939},[2009],[1840,2941,2328],{"className":2942},[1885],[1796,2944,2945,2946,3033],{},"在等可能有限样本空间中才可使用 ",[1840,2947,2949,2987],{"className":2948},[1843],[1840,2950,2952],{"className":2951},[1847],[1849,2953,2954],{"xmlns":1851},[1853,2955,2956,2984],{},[1856,2957,2958,2960,2962,2964,2966,2968,2971,2973,2975,2978,2980,2982],{},[1859,2959,1965],{},[1903,2961,1969],{"stretchy":1968},[1859,2963,1901],{},[1903,2965,1974],{"stretchy":1968},[1903,2967,2054],{},[1859,2969,2970],{"mathvariant":1861},"∣",[1859,2972,1901],{},[1859,2974,2970],{"mathvariant":1861},[1859,2976,2977],{"mathvariant":1861},"\u002F",[1859,2979,2970],{"mathvariant":1861},[1859,2981,1862],{"mathvariant":1861},[1859,2983,2970],{"mathvariant":1861},[1864,2985,2986],{"encoding":1866},"P(A)=|A|\u002F|\\Omega|",[1840,2988,2990,3017],{"className":2989,"ariaHidden":1872},[1871],[1840,2991,2993,2996,2999,3002,3005,3008,3011,3014],{"className":2992},[1876],[1840,2994],{"className":2995,"style":1994},[1880],[1840,2997,1965],{"className":2998,"style":1998},[1885,1924],[1840,3000,1969],{"className":3001},[2002],[1840,3003,1901],{"className":3004},[1885,1924],[1840,3006,1974],{"className":3007},[2009],[1840,3009],{"className":3010,"style":1929},[1928],[1840,3012,2054],{"className":3013},[1933],[1840,3015],{"className":3016,"style":1929},[1928],[1840,3018,3020,3023,3026,3029],{"className":3019},[1876],[1840,3021],{"className":3022,"style":1994},[1880],[1840,3024,2970],{"className":3025},[1885],[1840,3027,1901],{"className":3028},[1885,1924],[1840,3030,3032],{"className":3031},[1885],"∣\u002F∣Ω∣","。现实中的医学状态、金融损失或天气路径通常不是等可能计数问题。",[1807,3035,3037],{"id":3036},"_2-条件概率改变了参照总体","2. 条件概率改变了参照总体",[1840,3039,3041],{"className":3040},[2268],[1840,3042,3044,3116],{"className":3043},[1843],[1840,3045,3047],{"className":3046},[1847],[1849,3048,3049],{"xmlns":1851,"display":2277},[1853,3050,3051,3113],{},[1856,3052,3053,3055,3057,3059,3061,3063,3065,3067,3094,3096,3099,3101,3103,3105,3107,3110],{},[1859,3054,1965],{},[1903,3056,1969],{"stretchy":1968},[1859,3058,1901],{},[1903,3060,2970],{},[1859,3062,2757],{},[1903,3064,1974],{"stretchy":1968},[1903,3066,2054],{},[3068,3069,3070,3084],"mfrac",{},[1856,3071,3072,3074,3076,3078,3080,3082],{},[1859,3073,1965],{},[1903,3075,1969],{"stretchy":1968},[1859,3077,1901],{},[1903,3079,2791],{},[1859,3081,2757],{},[1903,3083,1974],{"stretchy":1968},[1856,3085,3086,3088,3090,3092],{},[1859,3087,1965],{},[1903,3089,1969],{"stretchy":1968},[1859,3091,2757],{},[1903,3093,1974],{"stretchy":1968},[1903,3095,2124],{"separator":1872},[1928,3097],{"width":3098},"2em",[1859,3100,1965],{},[1903,3102,1969],{"stretchy":1968},[1859,3104,2757],{},[1903,3106,1974],{"stretchy":1968},[1903,3108,3109],{},">",[1979,3111,3112],{},"0.",[1864,3114,3115],{"encoding":1866},"P(A\\mid B)=\\frac{P(A\\cap B)}{P(B)},\\qquad P(B)>0.",[1840,3117,3119,3143,3164,3303],{"className":3118,"ariaHidden":1872},[1871],[1840,3120,3122,3125,3128,3131,3134,3137,3140],{"className":3121},[1876],[1840,3123],{"className":3124,"style":1994},[1880],[1840,3126,1965],{"className":3127,"style":1998},[1885,1924],[1840,3129,1969],{"className":3130},[2002],[1840,3132,1901],{"className":3133},[1885,1924],[1840,3135],{"className":3136,"style":1929},[1928],[1840,3138,2970],{"className":3139},[1933],[1840,3141],{"className":3142,"style":1929},[1928],[1840,3144,3146,3149,3152,3155,3158,3161],{"className":3145},[1876],[1840,3147],{"className":3148,"style":1994},[1880],[1840,3150,2757],{"className":3151,"style":2837},[1885,1924],[1840,3153,1974],{"className":3154},[2009],[1840,3156],{"className":3157,"style":1929},[1928],[1840,3159,2054],{"className":3160},[1933],[1840,3162],{"className":3163,"style":1929},[1928],[1840,3165,3167,3171,3272,3275,3279,3282,3285,3288,3291,3294,3297,3300],{"className":3166},[1876],[1840,3168],{"className":3169,"style":3170},[1880],"height:2.363em;vertical-align:-0.936em;",[1840,3172,3174,3178,3269],{"className":3173},[1885],[1840,3175],{"className":3176},[2002,3177],"nulldelimiter",[1840,3179,3181],{"className":3180},[3068],[1840,3182,3184,3260],{"className":3183},[2163,2164],[1840,3185,3187,3257],{"className":3186},[2168],[1840,3188,3191,3213,3224],{"className":3189,"style":3190},[2172],"height:1.427em;",[1840,3192,3194,3198],{"style":3193},"top:-2.314em;",[1840,3195],{"className":3196,"style":3197},[2180],"height:3em;",[1840,3199,3201,3204,3207,3210],{"className":3200},[1885],[1840,3202,1965],{"className":3203,"style":1998},[1885,1924],[1840,3205,1969],{"className":3206},[2002],[1840,3208,2757],{"className":3209,"style":2837},[1885,1924],[1840,3211,1974],{"className":3212},[2009],[1840,3214,3216,3219],{"style":3215},"top:-3.23em;",[1840,3217],{"className":3218,"style":3197},[2180],[1840,3220],{"className":3221,"style":3223},[3222],"frac-line","border-bottom-width:0.04em;",[1840,3225,3227,3230],{"style":3226},"top:-3.677em;",[1840,3228],{"className":3229,"style":3197},[2180],[1840,3231,3233,3236,3239,3242,3245,3248,3251,3254],{"className":3232},[1885],[1840,3234,1965],{"className":3235,"style":1998},[1885,1924],[1840,3237,1969],{"className":3238},[2002],[1840,3240,1901],{"className":3241},[1885,1924],[1840,3243],{"className":3244,"style":2702},[1928],[1840,3246,2791],{"className":3247},[2706],[1840,3249],{"className":3250,"style":2702},[1928],[1840,3252,2757],{"className":3253,"style":2837},[1885,1924],[1840,3255,1974],{"className":3256},[2009],[1840,3258,2196],{"className":3259},[2195],[1840,3261,3263],{"className":3262},[2168],[1840,3264,3267],{"className":3265,"style":3266},[2172],"height:0.936em;",[1840,3268],{},[1840,3270],{"className":3271},[2009,3177],[1840,3273,2124],{"className":3274},[2209],[1840,3276],{"className":3277,"style":3278},[1928],"margin-right:2em;",[1840,3280],{"className":3281,"style":2213},[1928],[1840,3283,1965],{"className":3284,"style":1998},[1885,1924],[1840,3286,1969],{"className":3287},[2002],[1840,3289,2757],{"className":3290,"style":2837},[1885,1924],[1840,3292,1974],{"className":3293},[2009],[1840,3295],{"className":3296,"style":1929},[1928],[1840,3298,3109],{"className":3299},[1933],[1840,3301],{"className":3302,"style":1929},[1928],[1840,3304,3306,3309],{"className":3305},[1876],[1840,3307],{"className":3308,"style":2025},[1880],[1840,3310,3112],{"className":3311},[1885],[1796,3313,3314],{},"乘法公式：",[1840,3316,3318],{"className":3317},[2268],[1840,3319,3321,3369],{"className":3320},[1843],[1840,3322,3324],{"className":3323},[1847],[1849,3325,3326],{"xmlns":1851,"display":2277},[1853,3327,3328,3366],{},[1856,3329,3330,3332,3334,3336,3338,3340,3342,3344,3346,3348,3350,3352,3354,3356,3358,3360,3362,3364],{},[1859,3331,1965],{},[1903,3333,1969],{"stretchy":1968},[1859,3335,1901],{},[1903,3337,2791],{},[1859,3339,2757],{},[1903,3341,1974],{"stretchy":1968},[1903,3343,2054],{},[1859,3345,1965],{},[1903,3347,1969],{"stretchy":1968},[1859,3349,1901],{},[1903,3351,2970],{},[1859,3353,2757],{},[1903,3355,1974],{"stretchy":1968},[1859,3357,1965],{},[1903,3359,1969],{"stretchy":1968},[1859,3361,2757],{},[1903,3363,1974],{"stretchy":1968},[1859,3365,2328],{"mathvariant":1861},[1864,3367,3368],{"encoding":1866},"P(A\\cap B)=P(A\\mid B)P(B).",[1840,3370,3372,3396,3417,3441],{"className":3371,"ariaHidden":1872},[1871],[1840,3373,3375,3378,3381,3384,3387,3390,3393],{"className":3374},[1876],[1840,3376],{"className":3377,"style":1994},[1880],[1840,3379,1965],{"className":3380,"style":1998},[1885,1924],[1840,3382,1969],{"className":3383},[2002],[1840,3385,1901],{"className":3386},[1885,1924],[1840,3388],{"className":3389,"style":2702},[1928],[1840,3391,2791],{"className":3392},[2706],[1840,3394],{"className":3395,"style":2702},[1928],[1840,3397,3399,3402,3405,3408,3411,3414],{"className":3398},[1876],[1840,3400],{"className":3401,"style":1994},[1880],[1840,3403,2757],{"className":3404,"style":2837},[1885,1924],[1840,3406,1974],{"className":3407},[2009],[1840,3409],{"className":3410,"style":1929},[1928],[1840,3412,2054],{"className":3413},[1933],[1840,3415],{"className":3416,"style":1929},[1928],[1840,3418,3420,3423,3426,3429,3432,3435,3438],{"className":3419},[1876],[1840,3421],{"className":3422,"style":1994},[1880],[1840,3424,1965],{"className":3425,"style":1998},[1885,1924],[1840,3427,1969],{"className":3428},[2002],[1840,3430,1901],{"className":3431},[1885,1924],[1840,3433],{"className":3434,"style":1929},[1928],[1840,3436,2970],{"className":3437},[1933],[1840,3439],{"className":3440,"style":1929},[1928],[1840,3442,3444,3447,3450,3453,3456,3459,3462,3465],{"className":3443},[1876],[1840,3445],{"className":3446,"style":1994},[1880],[1840,3448,2757],{"className":3449,"style":2837},[1885,1924],[1840,3451,1974],{"className":3452},[2009],[1840,3454,1965],{"className":3455,"style":1998},[1885,1924],[1840,3457,1969],{"className":3458},[2002],[1840,3460,2757],{"className":3461,"style":2837},[1885,1924],[1840,3463,1974],{"className":3464},[2009],[1840,3466,2328],{"className":3467},[1885],[1796,3469,3470,3471,3537,3538,3604],{},"条件概率 ",[1840,3472,3474,3498],{"className":3473},[1843],[1840,3475,3477],{"className":3476},[1847],[1849,3478,3479],{"xmlns":1851},[1853,3480,3481,3495],{},[1856,3482,3483,3485,3487,3489,3491,3493],{},[1859,3484,1965],{},[1903,3486,1969],{"stretchy":1968},[1859,3488,1901],{},[1903,3490,2970],{},[1859,3492,2757],{},[1903,3494,1974],{"stretchy":1968},[1864,3496,3497],{"encoding":1866},"P(A\\mid B)",[1840,3499,3501,3525],{"className":3500,"ariaHidden":1872},[1871],[1840,3502,3504,3507,3510,3513,3516,3519,3522],{"className":3503},[1876],[1840,3505],{"className":3506,"style":1994},[1880],[1840,3508,1965],{"className":3509,"style":1998},[1885,1924],[1840,3511,1969],{"className":3512},[2002],[1840,3514,1901],{"className":3515},[1885,1924],[1840,3517],{"className":3518,"style":1929},[1928],[1840,3520,2970],{"className":3521},[1933],[1840,3523],{"className":3524,"style":1929},[1928],[1840,3526,3528,3531,3534],{"className":3527},[1876],[1840,3529],{"className":3530,"style":1994},[1880],[1840,3532,2757],{"className":3533,"style":2837},[1885,1924],[1840,3535,1974],{"className":3536},[2009]," 与反向条件概率 ",[1840,3539,3541,3565],{"className":3540},[1843],[1840,3542,3544],{"className":3543},[1847],[1849,3545,3546],{"xmlns":1851},[1853,3547,3548,3562],{},[1856,3549,3550,3552,3554,3556,3558,3560],{},[1859,3551,1965],{},[1903,3553,1969],{"stretchy":1968},[1859,3555,2757],{},[1903,3557,2970],{},[1859,3559,1901],{},[1903,3561,1974],{"stretchy":1968},[1864,3563,3564],{"encoding":1866},"P(B\\mid A)",[1840,3566,3568,3592],{"className":3567,"ariaHidden":1872},[1871],[1840,3569,3571,3574,3577,3580,3583,3586,3589],{"className":3570},[1876],[1840,3572],{"className":3573,"style":1994},[1880],[1840,3575,1965],{"className":3576,"style":1998},[1885,1924],[1840,3578,1969],{"className":3579},[2002],[1840,3581,2757],{"className":3582,"style":2837},[1885,1924],[1840,3584],{"className":3585,"style":1929},[1928],[1840,3587,2970],{"className":3588},[1933],[1840,3590],{"className":3591,"style":1929},[1928],[1840,3593,3595,3598,3601],{"className":3594},[1876],[1840,3596],{"className":3597,"style":1994},[1880],[1840,3599,1901],{"className":3600},[1885,1924],[1840,3602,1974],{"className":3603},[2009]," 通常不同。检测灵敏度是“患病条件下阳性”，病后概率是“阳性条件下患病”。",[1807,3606,3608],{"id":3607},"_3-独立不是互斥","3. 独立不是互斥",[1840,3610,3612],{"className":3611},[2268],[1840,3613,3615,3674],{"className":3614},[1843],[1840,3616,3618],{"className":3617},[1847],[1849,3619,3620],{"xmlns":1851,"display":2277},[1853,3621,3622,3671],{},[1856,3623,3624,3626,3629,3631,3634,3637,3639,3641,3643,3645,3647,3649,3651,3653,3655,3657,3659,3661,3663,3665,3667,3669],{},[1859,3625,1901],{},[1903,3627,3628],{},"⊥",[1859,3630,2757],{},[1928,3632],{"width":3633},"1em",[1903,3635,3636],{},"⟺",[1928,3638],{"width":3633},[1859,3640,1965],{},[1903,3642,1969],{"stretchy":1968},[1859,3644,1901],{},[1903,3646,2791],{},[1859,3648,2757],{},[1903,3650,1974],{"stretchy":1968},[1903,3652,2054],{},[1859,3654,1965],{},[1903,3656,1969],{"stretchy":1968},[1859,3658,1901],{},[1903,3660,1974],{"stretchy":1968},[1859,3662,1965],{},[1903,3664,1969],{"stretchy":1968},[1859,3666,2757],{},[1903,3668,1974],{"stretchy":1968},[1859,3670,2328],{"mathvariant":1861},[1864,3672,3673],{"encoding":1866},"A\\perp B\n\\quad\\Longleftrightarrow\\quad\nP(A\\cap B)=P(A)P(B).",[1840,3675,3677,3696,3722,3746,3767],{"className":3676,"ariaHidden":1872},[1871],[1840,3678,3680,3684,3687,3690,3693],{"className":3679},[1876],[1840,3681],{"className":3682,"style":3683},[1880],"height:0.6944em;",[1840,3685,1901],{"className":3686},[1885,1924],[1840,3688],{"className":3689,"style":1929},[1928],[1840,3691,3628],{"className":3692},[1933],[1840,3694],{"className":3695,"style":1929},[1928],[1840,3697,3699,3703,3706,3710,3713,3716,3719],{"className":3698},[1876],[1840,3700],{"className":3701,"style":3702},[1880],"height:0.7073em;vertical-align:-0.024em;",[1840,3704,2757],{"className":3705,"style":2837},[1885,1924],[1840,3707],{"className":3708,"style":3709},[1928],"margin-right:1em;",[1840,3711],{"className":3712,"style":1929},[1928],[1840,3714,3636],{"className":3715},[1933],[1840,3717],{"className":3718,"style":3709},[1928],[1840,3720],{"className":3721,"style":1929},[1928],[1840,3723,3725,3728,3731,3734,3737,3740,3743],{"className":3724},[1876],[1840,3726],{"className":3727,"style":1994},[1880],[1840,3729,1965],{"className":3730,"style":1998},[1885,1924],[1840,3732,1969],{"className":3733},[2002],[1840,3735,1901],{"className":3736},[1885,1924],[1840,3738],{"className":3739,"style":2702},[1928],[1840,3741,2791],{"className":3742},[2706],[1840,3744],{"className":3745,"style":2702},[1928],[1840,3747,3749,3752,3755,3758,3761,3764],{"className":3748},[1876],[1840,3750],{"className":3751,"style":1994},[1880],[1840,3753,2757],{"className":3754,"style":2837},[1885,1924],[1840,3756,1974],{"className":3757},[2009],[1840,3759],{"className":3760,"style":1929},[1928],[1840,3762,2054],{"className":3763},[1933],[1840,3765],{"className":3766,"style":1929},[1928],[1840,3768,3770,3773,3776,3779,3782,3785,3788,3791,3794,3797],{"className":3769},[1876],[1840,3771],{"className":3772,"style":1994},[1880],[1840,3774,1965],{"className":3775,"style":1998},[1885,1924],[1840,3777,1969],{"className":3778},[2002],[1840,3780,1901],{"className":3781},[1885,1924],[1840,3783,1974],{"className":3784},[2009],[1840,3786,1965],{"className":3787,"style":1998},[1885,1924],[1840,3789,1969],{"className":3790},[2002],[1840,3792,2757],{"className":3793,"style":2837},[1885,1924],[1840,3795,1974],{"className":3796},[2009],[1840,3798,2328],{"className":3799},[1885],[1796,3801,3802,3803,3845,3846,3874,3875,3903],{},"若 ",[1840,3804,3806,3824],{"className":3805},[1843],[1840,3807,3809],{"className":3808},[1847],[1849,3810,3811],{"xmlns":1851},[1853,3812,3813,3821],{},[1856,3814,3815,3817,3819],{},[1859,3816,1901],{},[1903,3818,2124],{"separator":1872},[1859,3820,2757],{},[1864,3822,3823],{"encoding":1866},"A,B",[1840,3825,3827],{"className":3826,"ariaHidden":1872},[1871],[1840,3828,3830,3833,3836,3839,3842],{"className":3829},[1876],[1840,3831],{"className":3832,"style":2149},[1880],[1840,3834,1901],{"className":3835},[1885,1924],[1840,3837,2124],{"className":3838},[2209],[1840,3840],{"className":3841,"style":2213},[1928],[1840,3843,2757],{"className":3844,"style":2837},[1885,1924]," 互斥且概率都为正，则知道 ",[1840,3847,3849,3862],{"className":3848},[1843],[1840,3850,3852],{"className":3851},[1847],[1849,3853,3854],{"xmlns":1851},[1853,3855,3856,3860],{},[1856,3857,3858],{},[1859,3859,1901],{},[1864,3861,1901],{"encoding":1866},[1840,3863,3865],{"className":3864,"ariaHidden":1872},[1871],[1840,3866,3868,3871],{"className":3867},[1876],[1840,3869],{"className":3870,"style":1881},[1880],[1840,3872,1901],{"className":3873},[1885,1924]," 发生会排除 ",[1840,3876,3878,3891],{"className":3877},[1843],[1840,3879,3881],{"className":3880},[1847],[1849,3882,3883],{"xmlns":1851},[1853,3884,3885,3889],{},[1856,3886,3887],{},[1859,3888,2757],{},[1864,3890,2757],{"encoding":1866},[1840,3892,3894],{"className":3893,"ariaHidden":1872},[1871],[1840,3895,3897,3900],{"className":3896},[1876],[1840,3898],{"className":3899,"style":1881},[1880],[1840,3901,2757],{"className":3902,"style":2837},[1885,1924],"，所以它们不独立。独立表示获知一个事件不改变另一个事件的概率。",[1796,3905,3906],{},"两两独立也不保证相互独立。研究多个变量时必须说明是哪一级独立性。",[1807,3908,3910],{"id":3909},"_4-全概率与贝叶斯公式","4. 全概率与贝叶斯公式",[1796,3912,3802,3913,4057],{},[1840,3914,3916,3947],{"className":3915},[1843],[1840,3917,3919],{"className":3918},[1847],[1849,3920,3921],{"xmlns":1851},[1853,3922,3923,3944],{},[1856,3924,3925,3931,3933,3935,3937],{},[2116,3926,3927,3929],{},[1859,3928,2757],{},[1979,3930,2057],{},[1903,3932,2124],{"separator":1872},[1903,3934,2136],{},[1903,3936,2124],{"separator":1872},[2116,3938,3939,3941],{},[1859,3940,2757],{},[1859,3942,3943],{},"k",[1864,3945,3946],{"encoding":1866},"B_1,\\ldots,B_k",[1840,3948,3950],{"className":3949,"ariaHidden":1872},[1871],[1840,3951,3953,3956,3997,4000,4003,4006,4009,4012,4015],{"className":3952},[1876],[1840,3954],{"className":3955,"style":2149},[1880],[1840,3957,3959,3962],{"className":3958},[1885],[1840,3960,2757],{"className":3961,"style":2837},[1885,1924],[1840,3963,3965],{"className":3964},[2159],[1840,3966,3968,3989],{"className":3967},[2163,2164],[1840,3969,3971,3986],{"className":3970},[2168],[1840,3972,3974],{"className":3973,"style":2173},[2172],[1840,3975,3977,3980],{"style":3976},"top:-2.55em;margin-left:-0.0502em;margin-right:0.05em;",[1840,3978],{"className":3979,"style":2181},[2180],[1840,3981,3983],{"className":3982},[2185,2186,2187,2188],[1840,3984,2057],{"className":3985},[1885,2188],[1840,3987,2196],{"className":3988},[2195],[1840,3990,3992],{"className":3991},[2168],[1840,3993,3995],{"className":3994,"style":2203},[2172],[1840,3996],{},[1840,3998,2124],{"className":3999},[2209],[1840,4001],{"className":4002,"style":2213},[1928],[1840,4004,2136],{"className":4005},[2263],[1840,4007],{"className":4008,"style":2213},[1928],[1840,4010,2124],{"className":4011},[2209],[1840,4013],{"className":4014,"style":2213},[1928],[1840,4016,4018,4021],{"className":4017},[1885],[1840,4019,2757],{"className":4020,"style":2837},[1885,1924],[1840,4022,4024],{"className":4023},[2159],[1840,4025,4027,4049],{"className":4026},[2163,2164],[1840,4028,4030,4046],{"className":4029},[2168],[1840,4031,4034],{"className":4032,"style":4033},[2172],"height:0.3361em;",[1840,4035,4036,4039],{"style":3976},[1840,4037],{"className":4038,"style":2181},[2180],[1840,4040,4042],{"className":4041},[2185,2186,2187,2188],[1840,4043,3943],{"className":4044,"style":4045},[1885,1924,2188],"margin-right:0.0315em;",[1840,4047,2196],{"className":4048},[2195],[1840,4050,4052],{"className":4051},[2168],[1840,4053,4055],{"className":4054,"style":2203},[2172],[1840,4056],{}," 构成互斥且完备的划分：",[1840,4059,4061],{"className":4060},[2268],[1840,4062,4064,4132],{"className":4063},[1843],[1840,4065,4067],{"className":4066},[1847],[1849,4068,4069],{"xmlns":1851,"display":2277},[1853,4070,4071,4129],{},[1856,4072,4073,4075,4077,4079,4081,4083,4099,4101,4103,4105,4107,4113,4115,4117,4119,4125,4127],{},[1859,4074,1965],{},[1903,4076,1969],{"stretchy":1968},[1859,4078,1901],{},[1903,4080,1974],{"stretchy":1968},[1903,4082,2054],{},[4084,4085,4086,4088,4097],"munderover",{},[1903,4087,2311],{},[1856,4089,4090,4093,4095],{},[1859,4091,4092],{},"j",[1903,4094,2054],{},[1979,4096,2057],{},[1859,4098,3943],{},[1859,4100,1965],{},[1903,4102,1969],{"stretchy":1968},[1859,4104,1901],{},[1903,4106,2970],{},[2116,4108,4109,4111],{},[1859,4110,2757],{},[1859,4112,4092],{},[1903,4114,1974],{"stretchy":1968},[1859,4116,1965],{},[1903,4118,1969],{"stretchy":1968},[2116,4120,4121,4123],{},[1859,4122,2757],{},[1859,4124,4092],{},[1903,4126,1974],{"stretchy":1968},[1859,4128,2328],{"mathvariant":1861},[1864,4130,4131],{"encoding":1866},"P(A)=\\sum_{j=1}^kP(A\\mid B_j)P(B_j).",[1840,4133,4135,4162,4258],{"className":4134,"ariaHidden":1872},[1871],[1840,4136,4138,4141,4144,4147,4150,4153,4156,4159],{"className":4137},[1876],[1840,4139],{"className":4140,"style":1994},[1880],[1840,4142,1965],{"className":4143,"style":1998},[1885,1924],[1840,4145,1969],{"className":4146},[2002],[1840,4148,1901],{"className":4149},[1885,1924],[1840,4151,1974],{"className":4152},[2009],[1840,4154],{"className":4155,"style":1929},[1928],[1840,4157,2054],{"className":4158},[1933],[1840,4160],{"className":4161,"style":1929},[1928],[1840,4163,4165,4169,4237,4240,4243,4246,4249,4252,4255],{"className":4164},[1876],[1840,4166],{"className":4167,"style":4168},[1880],"height:3.2499em;vertical-align:-1.4138em;",[1840,4170,4172],{"className":4171},[2364,2365],[1840,4173,4175,4228],{"className":4174},[2163,2164],[1840,4176,4178,4225],{"className":4177},[2168],[1840,4179,4182,4203,4213],{"className":4180,"style":4181},[2172],"height:1.8361em;",[1840,4183,4184,4187],{"style":2378},[1840,4185],{"className":4186,"style":2382},[2180],[1840,4188,4190],{"className":4189},[2185,2186,2187,2188],[1840,4191,4193,4197,4200],{"className":4192},[1885,2188],[1840,4194,4092],{"className":4195,"style":4196},[1885,1924,2188],"margin-right:0.0572em;",[1840,4198,2054],{"className":4199},[1933,2188],[1840,4201,2057],{"className":4202},[1885,2188],[1840,4204,4205,4208],{"style":2391},[1840,4206],{"className":4207,"style":2382},[2180],[1840,4209,4210],{},[1840,4211,2311],{"className":4212},[2364,2400,2401],[1840,4214,4216,4219],{"style":4215},"top:-4.3em;margin-left:0em;",[1840,4217],{"className":4218,"style":2382},[2180],[1840,4220,4222],{"className":4221},[2185,2186,2187,2188],[1840,4223,3943],{"className":4224,"style":4045},[1885,1924,2188],[1840,4226,2196],{"className":4227},[2195],[1840,4229,4231],{"className":4230},[2168],[1840,4232,4235],{"className":4233,"style":4234},[2172],"height:1.4138em;",[1840,4236],{},[1840,4238],{"className":4239,"style":2213},[1928],[1840,4241,1965],{"className":4242,"style":1998},[1885,1924],[1840,4244,1969],{"className":4245},[2002],[1840,4247,1901],{"className":4248},[1885,1924],[1840,4250],{"className":4251,"style":1929},[1928],[1840,4253,2970],{"className":4254},[1933],[1840,4256],{"className":4257,"style":1929},[1928],[1840,4259,4261,4265,4306,4309,4312,4315,4355,4358],{"className":4260},[1876],[1840,4262],{"className":4263,"style":4264},[1880],"height:1.0361em;vertical-align:-0.2861em;",[1840,4266,4268,4271],{"className":4267},[1885],[1840,4269,2757],{"className":4270,"style":2837},[1885,1924],[1840,4272,4274],{"className":4273},[2159],[1840,4275,4277,4297],{"className":4276},[2163,2164],[1840,4278,4280,4294],{"className":4279},[2168],[1840,4281,4283],{"className":4282,"style":2435},[2172],[1840,4284,4285,4288],{"style":3976},[1840,4286],{"className":4287,"style":2181},[2180],[1840,4289,4291],{"className":4290},[2185,2186,2187,2188],[1840,4292,4092],{"className":4293,"style":4196},[1885,1924,2188],[1840,4295,2196],{"className":4296},[2195],[1840,4298,4300],{"className":4299},[2168],[1840,4301,4304],{"className":4302,"style":4303},[2172],"height:0.2861em;",[1840,4305],{},[1840,4307,1974],{"className":4308},[2009],[1840,4310,1965],{"className":4311,"style":1998},[1885,1924],[1840,4313,1969],{"className":4314},[2002],[1840,4316,4318,4321],{"className":4317},[1885],[1840,4319,2757],{"className":4320,"style":2837},[1885,1924],[1840,4322,4324],{"className":4323},[2159],[1840,4325,4327,4347],{"className":4326},[2163,2164],[1840,4328,4330,4344],{"className":4329},[2168],[1840,4331,4333],{"className":4332,"style":2435},[2172],[1840,4334,4335,4338],{"style":3976},[1840,4336],{"className":4337,"style":2181},[2180],[1840,4339,4341],{"className":4340},[2185,2186,2187,2188],[1840,4342,4092],{"className":4343,"style":4196},[1885,1924,2188],[1840,4345,2196],{"className":4346},[2195],[1840,4348,4350],{"className":4349},[2168],[1840,4351,4353],{"className":4352,"style":4303},[2172],[1840,4354],{},[1840,4356,1974],{"className":4357},[2009],[1840,4359,2328],{"className":4360},[1885],[1796,4362,4363],{},"贝叶斯公式：",[1840,4365,4367],{"className":4366},[2268],[1840,4368,4370,4479],{"className":4369},[1843],[1840,4371,4373],{"className":4372},[1847],[1849,4374,4375],{"xmlns":1851,"display":2277},[1853,4376,4377,4476],{},[1856,4378,4379,4381,4383,4389,4391,4393,4395,4397,4474],{},[1859,4380,1965],{},[1903,4382,1969],{"stretchy":1968},[2116,4384,4385,4387],{},[1859,4386,2757],{},[1859,4388,4092],{},[1903,4390,2970],{},[1859,4392,1901],{},[1903,4394,1974],{"stretchy":1968},[1903,4396,2054],{},[3068,4398,4399,4429],{},[1856,4400,4401,4403,4405,4407,4409,4415,4417,4419,4421,4427],{},[1859,4402,1965],{},[1903,4404,1969],{"stretchy":1968},[1859,4406,1901],{},[1903,4408,2970],{},[2116,4410,4411,4413],{},[1859,4412,2757],{},[1859,4414,4092],{},[1903,4416,1974],{"stretchy":1968},[1859,4418,1965],{},[1903,4420,1969],{"stretchy":1968},[2116,4422,4423,4425],{},[1859,4424,2757],{},[1859,4426,4092],{},[1903,4428,1974],{"stretchy":1968},[1856,4430,4431,4446,4448,4450,4452,4454,4460,4462,4464,4466,4472],{},[4084,4432,4433,4435,4444],{},[1903,4434,2311],{},[1856,4436,4437,4440,4442],{},[1859,4438,4439],{"mathvariant":1861},"ℓ",[1903,4441,2054],{},[1979,4443,2057],{},[1859,4445,3943],{},[1859,4447,1965],{},[1903,4449,1969],{"stretchy":1968},[1859,4451,1901],{},[1903,4453,2970],{},[2116,4455,4456,4458],{},[1859,4457,2757],{},[1859,4459,4439],{"mathvariant":1861},[1903,4461,1974],{"stretchy":1968},[1859,4463,1965],{},[1903,4465,1969],{"stretchy":1968},[2116,4467,4468,4470],{},[1859,4469,2757],{},[1859,4471,4439],{"mathvariant":1861},[1903,4473,1974],{"stretchy":1968},[1859,4475,2328],{"mathvariant":1861},[1864,4477,4478],{"encoding":1866},"P(B_j\\mid A)\n=\n\\frac{P(A\\mid B_j)P(B_j)}\n{\\sum_{\\ell=1}^kP(A\\mid B_\\ell)P(B_\\ell)}.",[1840,4480,4482,4543,4564],{"className":4481,"ariaHidden":1872},[1871],[1840,4483,4485,4488,4491,4494,4534,4537,4540],{"className":4484},[1876],[1840,4486],{"className":4487,"style":4264},[1880],[1840,4489,1965],{"className":4490,"style":1998},[1885,1924],[1840,4492,1969],{"className":4493},[2002],[1840,4495,4497,4500],{"className":4496},[1885],[1840,4498,2757],{"className":4499,"style":2837},[1885,1924],[1840,4501,4503],{"className":4502},[2159],[1840,4504,4506,4526],{"className":4505},[2163,2164],[1840,4507,4509,4523],{"className":4508},[2168],[1840,4510,4512],{"className":4511,"style":2435},[2172],[1840,4513,4514,4517],{"style":3976},[1840,4515],{"className":4516,"style":2181},[2180],[1840,4518,4520],{"className":4519},[2185,2186,2187,2188],[1840,4521,4092],{"className":4522,"style":4196},[1885,1924,2188],[1840,4524,2196],{"className":4525},[2195],[1840,4527,4529],{"className":4528},[2168],[1840,4530,4532],{"className":4531,"style":4303},[2172],[1840,4533],{},[1840,4535],{"className":4536,"style":1929},[1928],[1840,4538,2970],{"className":4539},[1933],[1840,4541],{"className":4542,"style":1929},[1928],[1840,4544,4546,4549,4552,4555,4558,4561],{"className":4545},[1876],[1840,4547],{"className":4548,"style":1994},[1880],[1840,4550,1901],{"className":4551},[1885,1924],[1840,4553,1974],{"className":4554},[2009],[1840,4556],{"className":4557,"style":1929},[1928],[1840,4559,2054],{"className":4560},[1933],[1840,4562],{"className":4563,"style":1929},[1928],[1840,4565,4567,4571,4918],{"className":4566},[1876],[1840,4568],{"className":4569,"style":4570},[1880],"height:2.6057em;vertical-align:-1.1787em;",[1840,4572,4574,4577,4915],{"className":4573},[1885],[1840,4575],{"className":4576},[2002,3177],[1840,4578,4580],{"className":4579},[3068],[1840,4581,4583,4906],{"className":4582},[2163,2164],[1840,4584,4586,4903],{"className":4585},[2168],[1840,4587,4589,4777,4785],{"className":4588,"style":3190},[2172],[1840,4590,4592,4595],{"style":4591},"top:-2.121em;",[1840,4593],{"className":4594,"style":3197},[2180],[1840,4596,4598,4664,4667,4670,4673,4676,4679,4682,4685,4725,4728,4731,4734,4774],{"className":4597},[1885],[1840,4599,4601,4606],{"className":4600},[2364],[1840,4602,2311],{"className":4603,"style":4605},[2364,2400,4604],"small-op","position:relative;top:0em;",[1840,4607,4609],{"className":4608},[2159],[1840,4610,4612,4655],{"className":4611},[2163,2164],[1840,4613,4615,4652],{"className":4614},[2168],[1840,4616,4619,4640],{"className":4617,"style":4618},[2172],"height:0.989em;",[1840,4620,4622,4625],{"style":4621},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1840,4623],{"className":4624,"style":2181},[2180],[1840,4626,4628],{"className":4627},[2185,2186,2187,2188],[1840,4629,4631,4634,4637],{"className":4630},[1885,2188],[1840,4632,4439],{"className":4633},[1885,2188],[1840,4635,2054],{"className":4636},[1933,2188],[1840,4638,2057],{"className":4639},[1885,2188],[1840,4641,4643,4646],{"style":4642},"top:-3.2029em;margin-right:0.05em;",[1840,4644],{"className":4645,"style":2181},[2180],[1840,4647,4649],{"className":4648},[2185,2186,2187,2188],[1840,4650,3943],{"className":4651,"style":4045},[1885,1924,2188],[1840,4653,2196],{"className":4654},[2195],[1840,4656,4658],{"className":4657},[2168],[1840,4659,4662],{"className":4660,"style":4661},[2172],"height:0.2997em;",[1840,4663],{},[1840,4665],{"className":4666,"style":2213},[1928],[1840,4668,1965],{"className":4669,"style":1998},[1885,1924],[1840,4671,1969],{"className":4672},[2002],[1840,4674,1901],{"className":4675},[1885,1924],[1840,4677],{"className":4678,"style":1929},[1928],[1840,4680,2970],{"className":4681},[1933],[1840,4683],{"className":4684,"style":1929},[1928],[1840,4686,4688,4691],{"className":4687},[1885],[1840,4689,2757],{"className":4690,"style":2837},[1885,1924],[1840,4692,4694],{"className":4693},[2159],[1840,4695,4697,4717],{"className":4696},[2163,2164],[1840,4698,4700,4714],{"className":4699},[2168],[1840,4701,4703],{"className":4702,"style":4033},[2172],[1840,4704,4705,4708],{"style":3976},[1840,4706],{"className":4707,"style":2181},[2180],[1840,4709,4711],{"className":4710},[2185,2186,2187,2188],[1840,4712,4439],{"className":4713},[1885,2188],[1840,4715,2196],{"className":4716},[2195],[1840,4718,4720],{"className":4719},[2168],[1840,4721,4723],{"className":4722,"style":2203},[2172],[1840,4724],{},[1840,4726,1974],{"className":4727},[2009],[1840,4729,1965],{"className":4730,"style":1998},[1885,1924],[1840,4732,1969],{"className":4733},[2002],[1840,4735,4737,4740],{"className":4736},[1885],[1840,4738,2757],{"className":4739,"style":2837},[1885,1924],[1840,4741,4743],{"className":4742},[2159],[1840,4744,4746,4766],{"className":4745},[2163,2164],[1840,4747,4749,4763],{"className":4748},[2168],[1840,4750,4752],{"className":4751,"style":4033},[2172],[1840,4753,4754,4757],{"style":3976},[1840,4755],{"className":4756,"style":2181},[2180],[1840,4758,4760],{"className":4759},[2185,2186,2187,2188],[1840,4761,4439],{"className":4762},[1885,2188],[1840,4764,2196],{"className":4765},[2195],[1840,4767,4769],{"className":4768},[2168],[1840,4770,4772],{"className":4771,"style":2203},[2172],[1840,4773],{},[1840,4775,1974],{"className":4776},[2009],[1840,4778,4779,4782],{"style":3215},[1840,4780],{"className":4781,"style":3197},[2180],[1840,4783],{"className":4784,"style":3223},[3222],[1840,4786,4787,4790],{"style":3226},[1840,4788],{"className":4789,"style":3197},[2180],[1840,4791,4793,4796,4799,4802,4805,4808,4811,4851,4854,4857,4860,4900],{"className":4792},[1885],[1840,4794,1965],{"className":4795,"style":1998},[1885,1924],[1840,4797,1969],{"className":4798},[2002],[1840,4800,1901],{"className":4801},[1885,1924],[1840,4803],{"className":4804,"style":1929},[1928],[1840,4806,2970],{"className":4807},[1933],[1840,4809],{"className":4810,"style":1929},[1928],[1840,4812,4814,4817],{"className":4813},[1885],[1840,4815,2757],{"className":4816,"style":2837},[1885,1924],[1840,4818,4820],{"className":4819},[2159],[1840,4821,4823,4843],{"className":4822},[2163,2164],[1840,4824,4826,4840],{"className":4825},[2168],[1840,4827,4829],{"className":4828,"style":2435},[2172],[1840,4830,4831,4834],{"style":3976},[1840,4832],{"className":4833,"style":2181},[2180],[1840,4835,4837],{"className":4836},[2185,2186,2187,2188],[1840,4838,4092],{"className":4839,"style":4196},[1885,1924,2188],[1840,4841,2196],{"className":4842},[2195],[1840,4844,4846],{"className":4845},[2168],[1840,4847,4849],{"className":4848,"style":4303},[2172],[1840,4850],{},[1840,4852,1974],{"className":4853},[2009],[1840,4855,1965],{"className":4856,"style":1998},[1885,1924],[1840,4858,1969],{"className":4859},[2002],[1840,4861,4863,4866],{"className":4862},[1885],[1840,4864,2757],{"className":4865,"style":2837},[1885,1924],[1840,4867,4869],{"className":4868},[2159],[1840,4870,4872,4892],{"className":4871},[2163,2164],[1840,4873,4875,4889],{"className":4874},[2168],[1840,4876,4878],{"className":4877,"style":2435},[2172],[1840,4879,4880,4883],{"style":3976},[1840,4881],{"className":4882,"style":2181},[2180],[1840,4884,4886],{"className":4885},[2185,2186,2187,2188],[1840,4887,4092],{"className":4888,"style":4196},[1885,1924,2188],[1840,4890,2196],{"className":4891},[2195],[1840,4893,4895],{"className":4894},[2168],[1840,4896,4898],{"className":4897,"style":4303},[2172],[1840,4899],{},[1840,4901,1974],{"className":4902},[2009],[1840,4904,2196],{"className":4905},[2195],[1840,4907,4909],{"className":4908},[2168],[1840,4910,4913],{"className":4911,"style":4912},[2172],"height:1.1787em;",[1840,4914],{},[1840,4916],{"className":4917},[2009,3177],[1840,4919,2328],{"className":4920},[1885],[1796,4922,4923],{},"它把先验基准率与新证据的似然结合。证据很准确时，低基准率仍可能让阳性结果中出现大量假阳性。",[1807,4925,4927],{"id":4926},"_5-可运行案例低患病率下的阳性预测值","5. 可运行案例：低患病率下的阳性预测值",[1796,4929,4930],{},"设患病率 1%、灵敏度 95%、特异度 90%。代码先算精确后验，再模拟 300,000 人。",[4932,4933],"pyodide",{"code64":4934,"layout":4935,"locale":7,"packages":4936,"title":4937},"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","vertical","numpy","Python：检测准确率、基准率与后验概率",[1796,4939,4940],{},"“95% 灵敏度”不能写成“阳性后有 95% 患病概率”。在这组参数下，大量健康人中的 10% 假阳性会超过少量患者中的真阳性。",[1807,4942,4944],{"id":4943},"_6-树形思维","6. 树形思维",[1796,4946,4947],{},"处理条件概率问题时先画路径：",[4949,4950],"mermaid-diagram",{"code64":4951,"locale":7},"Zmxvd2NoYXJ0IExSCiAgUFsi5Lq6576kIl0gLS0+IERbIuaCo+eXhSAxJSJdCiAgUCAtLT4gSFsi5YGl5bq3IDk5JSJdCiAgRCAtLT4gRFBbIumYs+aApyA5NSUiXQogIEQgLS0+IEROWyLpmLTmgKcgNSUiXQogIEggLS0+IEhQWyLpmLPmgKcgMTAlIl0KICBIIC0tPiBITlsi6Zi05oCnIDkwJSJd",[1796,4953,4954],{},"每条完整路径概率相乘，互斥路径概率相加。这样比直接套贝叶斯公式更不容易把条件方向颠倒。",[1807,4956,4958],{"id":4957},"_7-常见反直觉","7. 常见反直觉",[4960,4961,4962,4968,4974,4980],"ul",{},[1817,4963,4964,4967],{},[1799,4965,4966],{},"Monty Hall："," 主持人开门不是随机缺失，而是依赖奖品位置的信息机制。",[1817,4969,4970,4973],{},[1799,4971,4972],{},"生日问题："," 比较的是任意一对相同，不是某人与指定日期相同。",[1817,4975,4976,4979],{},[1799,4977,4978],{},"辛普森悖论："," 分层内关系与合并关系可相反，原因是组别构成变化。",[1817,4981,4982,4985],{},[1799,4983,4984],{},"重复检测："," 两次误差若受同一仪器或生理因素影响，不能简单按独立概率相乘。",[1807,4987,4989],{"id":4988},"_8-诊断清单","8. 诊断清单",[1814,4991,4992,4995,4998,5133,5136,5139],{},[1817,4993,4994],{},"样本空间是否完整且互斥？",[1817,4996,4997],{},"“给定”信息改变了哪个参照总体？",[1817,4999,5000,5001,5066,5067,5132],{},"是否把 ",[1840,5002,5004,5027],{"className":5003},[1843],[1840,5005,5007],{"className":5006},[1847],[1849,5008,5009],{"xmlns":1851},[1853,5010,5011,5025],{},[1856,5012,5013,5015,5017,5019,5021,5023],{},[1859,5014,1965],{},[1903,5016,1969],{"stretchy":1968},[1859,5018,1901],{},[1903,5020,2970],{},[1859,5022,2757],{},[1903,5024,1974],{"stretchy":1968},[1864,5026,3497],{"encoding":1866},[1840,5028,5030,5054],{"className":5029,"ariaHidden":1872},[1871],[1840,5031,5033,5036,5039,5042,5045,5048,5051],{"className":5032},[1876],[1840,5034],{"className":5035,"style":1994},[1880],[1840,5037,1965],{"className":5038,"style":1998},[1885,1924],[1840,5040,1969],{"className":5041},[2002],[1840,5043,1901],{"className":5044},[1885,1924],[1840,5046],{"className":5047,"style":1929},[1928],[1840,5049,2970],{"className":5050},[1933],[1840,5052],{"className":5053,"style":1929},[1928],[1840,5055,5057,5060,5063],{"className":5056},[1876],[1840,5058],{"className":5059,"style":1994},[1880],[1840,5061,2757],{"className":5062,"style":2837},[1885,1924],[1840,5064,1974],{"className":5065},[2009]," 与 ",[1840,5068,5070,5093],{"className":5069},[1843],[1840,5071,5073],{"className":5072},[1847],[1849,5074,5075],{"xmlns":1851},[1853,5076,5077,5091],{},[1856,5078,5079,5081,5083,5085,5087,5089],{},[1859,5080,1965],{},[1903,5082,1969],{"stretchy":1968},[1859,5084,2757],{},[1903,5086,2970],{},[1859,5088,1901],{},[1903,5090,1974],{"stretchy":1968},[1864,5092,3564],{"encoding":1866},[1840,5094,5096,5120],{"className":5095,"ariaHidden":1872},[1871],[1840,5097,5099,5102,5105,5108,5111,5114,5117],{"className":5098},[1876],[1840,5100],{"className":5101,"style":1994},[1880],[1840,5103,1965],{"className":5104,"style":1998},[1885,1924],[1840,5106,1969],{"className":5107},[2002],[1840,5109,2757],{"className":5110,"style":2837},[1885,1924],[1840,5112],{"className":5113,"style":1929},[1928],[1840,5115,2970],{"className":5116},[1933],[1840,5118],{"className":5119,"style":1929},[1928],[1840,5121,5123,5126,5129],{"className":5122},[1876],[1840,5124],{"className":5125,"style":1994},[1880],[1840,5127,1901],{"className":5128},[1885,1924],[1840,5130,1974],{"className":5131},[2009]," 混淆？",[1817,5134,5135],{},"独立性是制度假设、模型假设还是可检验证据？",[1817,5137,5138],{},"基准率来自目标人群还是另一个样本？",[1817,5140,5141],{},"数据缺失或选择机制是否携带信息？",[1807,5143,5144],{"id":5144},"课堂任务",[1796,5146,5147],{},"机场安检报警率为：危险品携带者中 98% 报警，普通旅客中 3% 报警；携带率为万分之一。",[1814,5149,5150,5153,5156,5159],{},[1817,5151,5152],{},"画概率树；",[1817,5154,5155],{},"计算报警后的携带概率；",[1817,5157,5158],{},"把普通旅客误报率降到 0.3% 后重算；",[1817,5160,5161],{},"说明为何连续两台机器的结果未必独立。",[1807,5163,5164],{"id":5164},"核心阅读",[4960,5166,5167,5181,5188],{},[1817,5168,5169,5170,5180],{},"Blitzstein & Hwang, ",[5171,5172,5176],"a",{"href":5173,"rel":5174},"https:\u002F\u002Fprojects.iq.harvard.edu\u002Fstat110\u002Fhome",[5175],"nofollow",[5177,5178,5179],"em",{},"Introduction to Probability","（含开放课程）。",[1817,5182,5183,5184,5187],{},"Ross, ",[5177,5185,5186],{},"A First Course in Probability","，条件概率与独立性章节。",[1817,5189,5190,5191,5194],{},"Bayes’ theorem 的现代解释可对照 Wasserman, ",[5177,5192,5193],{},"All of Statistics","，第 8 章。",[1796,5196,5197,5198,5202,5203,5207],{},"上一章：",[5171,5199,5201],{"href":5200},"..\u002F..\u002F00-intro\u002F","课程导论","｜下一章：",[5171,5204,5206],{"href":5205},"..\u002F02-random-variables\u002F","随机变量","。",{"title":10,"searchDepth":5209,"depth":5209,"links":5210},2,[5211,5212,5213,5214,5215,5216,5217,5218,5219,5220,5221],{"id":1809,"depth":5209,"text":1809},{"id":1834,"depth":5209,"text":1835},{"id":3036,"depth":5209,"text":3037},{"id":3607,"depth":5209,"text":3608},{"id":3909,"depth":5209,"text":3910},{"id":4926,"depth":5209,"text":4927},{"id":4943,"depth":5209,"text":4944},{"id":4957,"depth":5209,"text":4958},{"id":4988,"depth":5209,"text":4989},{"id":5144,"depth":5209,"text":5144},{"id":5164,"depth":5209,"text":5164},"从样本空间与概率公理进入条件概率、独立性、全概率和贝叶斯公式。","md",{"sidebar":5225},{"order":5209},true,{"title":1651,"description":5222},"AkjXe-WRVbIDZevnCaL5ZoY0Tm2znbB3cSHiq3bcuBI",[5230,5232],{"title":1640,"path":1641,"stem":1642,"description":5231,"children":-1},"用一次质量抽检串起总体、样本、随机变量、统计量、参数和不确定性。",{"title":1657,"path":1658,"stem":1659,"description":5233,"children":-1},"统一理解 PMF、PDF、CDF、分位数、联合分布、条件分布与变量变换。",1785754756259]