機率論 I
組合分析 Combinatorial Analysis
The Basic Principle of Counting
The Generalized Basic Principle of Counting
Permutations
Example
Combinations
The Binomial Theorem
Multinomial Coefficients
On the Distribution of Balls in Urns
機率公設 Axioms of Probability
Sample Sapce and Events
The Laws of Events
Commulative, Associative, Distributive and DeMorgan Laws
Axioms of Probability
Some Simple Propositions
Remark
Probability As a Continuous Set Function
Proposition
The Birthday Problem
The Matching Problem
條件機率與獨立 Conditionaly Probability and Independence
Conditional Probabilites
The Multiplication Rule
Bayes' Formula
Proposition
Independent
Independent Events
Example
P(*|F) Is a Probability
Proposition
Example
Conditionally Independent
The Problem of the Points
The Gambler's Ruin Problem
The Matching Problem
隨機變數 Random Variables
Random Variables
Example
Distribution Function
Discrete Random Variables
Cumulative Distribution Function
Expected Value
Expectation of a Function of a Random Variable
Variance
The Bernoulli and Binomial Random Variables
Example
Properties of Binomial Random Varables
Computing the Binomial Distribution Function
The Poisson Random Variable
The Expectation and Variance of Poisson Random Variable
Poisson Process
Example
The Geometric Probability Distributions
The Negative Binomial Random Variable
The Hypergeometric Random Variable
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