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.