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.