Tuesday, Feb 3

This is an outline of the topics we covered in class. These notes are not a substitute for your own note-taking. I highly recommend that you take your own notes during class. If you ever miss a class for any reason, reach out to another student in class to get a copy of their notes.

Variance

Question: How spread out are X values? One answer we might try is to measure the average distance from the average value: \E\left[|X - \E(X)|\right] To simplify notation, we'll write \mu = \E(X). Also, it's often usefull to square a term rather than take absolute value when we want to ensure a positive output, so we'll define...

Let X be a random variable with \E(X) = \mu. The variance of X is: \sigma^2 = \Var(x) = \E\left[ (X - \mu)^2\right] \sigma = \sqrt{\Var(X)} is called the standard deviation.