12. Standard Deviation

The expected value \(\mu_X\) of a random variable \(X\) is a measure of the center of the distribution of \(X\). But we know that \(X\) need not be equal to \(\mu_X\); indeed, \(\mu_X\) need not even be a possible value of \(X\).

How far from \(\mu_X\) can \(X\) be? This chapter develops an answer to that question, by examining the mean squared error familiar to you from Data 8.