[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Let [math]X[/math] be a random variable with [math]\mu = E(X)[/math] and

[math]\sigma^2 = V(X)[/math]. Define [math]X^* = (X - \mu)/\sigma[/math]. The random variable [math]X^*[/math] is called the standardized random variable associated with [math]X[/math]. Show that this standardized random variable has expected value 0 and variance 1.