[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 continuous random variable with mean [math]\mu(X)[/math] and variance

[math]\sigma^2(X)[/math], and let [math]X^* = (X - \mu)/\sigma[/math] be its standardized version. Verify directly that [math]\mu(X^*) = 0[/math] and [math]\sigma^2(X^*) = 1[/math].