# Chapter 5: Joint Probability Distributionscao/Teaching/Stat285/chapter5.pdf · Chapter 5: Joint...

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### Transcript of Chapter 5: Joint Probability Distributionscao/Teaching/Stat285/chapter5.pdf · Chapter 5: Joint...

Chapter 5: Joint Probability Distributions

Outline Jointly Distributed Random Variables

Outline Expected values, covariance and correlation

Outline Statistics and their distributions

Outline Distribution of the Sample Mean

Outline The Distribution of Linear Combinations

Joint Probability Mass Function

Joint Probability Density Function

Example of joint probability density

Marginal densities in example

Independent Random Variables

Conditional distributions

Expected value

Correlation

Random samples

Properties of sample mean and sample sum

Central Limit Theorem

Linear Combinations and their means

Variances of linear combinations

The difference between random variables

The Case of Normal Random Variables

Chapter 5: Joint Probability DistributionsOutline Jointly Distributed Random VariablesOutline Expected values, covariance and correlationOutline Statistics and their distributionsOutline Distribution of the Sample MeanOutline The Distribution of Linear CombinationsJoint Probability Mass FunctionJoint Probability Density FunctionExample of joint probability densityMarginal densities in exampleIndependent Random VariablesConditional distributionsExpected valueCorrelationRandom samplesProperties of sample mean and sample sumCentral Limit TheoremLinear Combinations and their meansVariances of linear combinationsThe difference between random variablesThe Case of Normal Random Variables