機率論 II
連續隨機變數 Continuous Random Variables
Continuous Random Variables
Expectation and Variance of Continuous Random Variables
Proposition
The Uniform Random Variable
Example
Normal Random Variables
Example
The Standard Normal Distribution
The Normal Approximation to the Binomial Distribution
Exponential Random Variables
Memoryless
Hazard Rate Functions
The Gamma Distribution
Other Continuous Distributions
The Distribution of a Function of a Random Variable
聯合分布隨機變數 Jointly Distributed Random Variables
Joint Cumulative Probability Distribution Functions
Example
Joint Distribution Functions
Example
Multinomial Distribution
Independent Random Variables
Characterization of the Normal Distribution
Independent of n random variables
Sums of Independent Random Variables
Family of Distribution
Chi-Squared Distribution
Proposition
Conditional Distributions - Discrete Case
Conditional Distribution - Continuous Case
onditional Distribution - Continuous Case and Discrete Case
Order Statistics
Example of Order Statistics
Joint Probability Distribution Functions of Random Variables
Generation of Normal Random Variables
Joint Probability Distribution Function on n-dimention
期望值的性質 Properties of Expectation
Introduction
Proposition
Example
Expectation of Sums of Random Variables
Problem I
Problem II
Problem III
Covariance, Variance of Sums
Example
Problem
Correlation
Conditional Expectation
Computing Expectations by Conditioning
Computing Probabilities by Conditioning
Conditional Variance
Conditional Expectation and Prediction
Linear Predictor
Moment Generating Functions
Property of Moment Generating Function
M.G.F of distribution
Additional Properties of Normal Random Variables
極限定理 Limit theorems
Chebyshev's Inequality and Weak Law of Large Numbers
The Central Limit Theorem
Other Inequalities
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