Several Random Variables

So far, we have mostly looked at random variables one at a time. In practice, however, we often need to deal with several random variables at once.

To describe how random variables behave together, we introduce joint probability distributions. We then look more closely at some important ways in which random variables can be related, including independence, covariance and correlation.

Finally, we develop some useful tools for working with combinations of random variables, including variance-covariance matrices, convolutions, and transformations of several random variables at once.

These ideas become especially important later in statistics and econometrics, where we routinely work with many variables together.