https://en.wikipedia.org/wiki/Law_of_total_probability the total probability of an outcome which can be realized via several distinct events - hence the name…

title: [概率论]2-1:条件概率(Conditional Probability) categories: Mathematic Probability keywords: Conditional Probability 条件概率 Multiplication Rule 乘法原理 Partitions Law of total Probability 全概率公式 toc: true date: 2018-01-31 10:34:36 Abstract: 本文介绍条件概率的定义及相关知识,…

Nice R Code Punning code better since 2013 RSS Blog Archives Guides Modules About Markov Chain Monte Carlo 10 JUNE 2013 This topic doesn’t have much to do with nicer code, but there is probably some overlap in interest. However, some of the topics th…

这里用Venn diagram来不严谨地推导一下贝叶斯定理. 假设A和B为两个不相互独立的事件. 交集(intersection):  上图红色部分即为事件A和事件B的交集. 并集(union):  由Venn diagram可以看出,在事件B已经发生的情况下,事件A发生的概率为事件A和事件B的交集除以事件B: 同理,在事件A已经发生的情况下,事件B发生的概率为事件A和事件B的交集除以事件A: 注:表示 A,B 事件同时发生的概率,如果 A 和 B 是相互独立的两个事件,那么:. 由上面的公式可…

I Proofs1 What is a Proof?2 The Well Ordering Principle3 Logical Formulas4 Mathematical Data Types5 Induction6 State Machines7 Recursive Data Types8 Infinite SetsII Structures9 Number Theory10 Directed graphs & Partial Orders11 Communication Networks…

title: [概率论]4-7:条件期望(Conditional Expectation) categories: - Mathematic - Probability keywords: - Expectation - Prediction - Law of total Probability toc: true date: 2018-03-27 10:53:24 Abstract: 本文介绍期望的条件版本,也就是条件期望 Keywords: Expectation,Prediction,La…

title: [概率论]3-7:多变量分布(Multivariate Distributions Part II) categories: Mathematic Probability keywords: Conditional Distributions 条件分布 Bayes' Theorem 贝叶斯理论 Histograms 直方图 Law of total Probability 全概率公式 toc: true date: 2018-03-15 09:20:38 Abstract: 本文继…

title: [概率论]3-6:条件分布(Conditional Distributions Part I) categories: Mathematic Probability keywords: Discrete Conditional Distributions 离散条件分布 Continuous Conditional Distributions 连续条件分布 toc: true date: 2018-03-08 10:38:13 Abstract: 首先介绍随机变量的条件分布,随后介绍…

title: [概率论]3-6:条件分布(Conditional Distributions Part II) categories: Mathematic Probability keywords: Multiplication Rule for Distributions 乘法法则 Bayes' Theorem 贝叶斯理论 Law of Total Probability for Random Variables 随机变量的全概率公式 toc: true date: 2018-03-12 0…

title: [概率论]2-3:贝叶斯定理(Bayes' Theorem) categories: Mathematic Probability keywords: Bayes' Theorem 贝叶斯公式 Law of total Probability 全概率公式 toc: true date: 2018-02-02 10:10:45 Abstract: 本文是关于Bayes' Theorem 的介绍性知识 Keywords: Bayes' Theorem,Law of total Prob…