Study Notes: Multivariate Random Variables

Chapter 4. Common Multivariate Random Variables Study Notes contains 21 pages covering the following learning objectives:

* Explain how a probability matrix can be used to express a probability mass function.

* Compute the marginal and conditional distributions of a discrete bivariate random variable.

* Explain how the expectation of a function is computed for a bivariate discrete random variable.

* Define covariance and explain what it measures.

* Explain the relationship between the covariance and correlation of two random variables, and how these are related to the independence of the two variables.

* Explain the effects of applying linear transformations on the covariance and correlation between two random variables.

* Compute the variance of a weighted sum of two random variables.

* Compute the conditional expectation of a component of a bivariate random variable.

* Describe the features of an iid sequence of random variables.

* Explain how the iid property is helpful in computing the mean and variance of a sum of iid random variables.

After reviewing these notes on Multivariate Random Variables, you will be able to apply what you learned with practice questions.

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