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