QA 4. Multivariate Random Variables

Learning Objectives

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

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

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

4) Define covariance and explain what it measures.

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

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

7) Compute the variance of a weighted sum of two random variables.

8) Compute the conditional expectation of a component of a bivariate random variable.

9) Describe the features of an independent and identically distributed (iid) sequence of random variables.

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