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In the discrete random variables section, we discussed how the expectation and variance of random variables are affected by scalar addition and multiplication. The idea of performing a "linear transformation" on a random variable is a very important one, and as such, statisticians have found rules that allow us to extend it beyond the "base case" of a single random variable.
We'll discuss how random variables can be combined and transformed together in this section, but first, let's quickly review how linear transformations work on a single random variable.