[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]

For each of the densities in Exercise Exercise calculate

the first and second moments, [math]\mu_1[/math] and [math]\mu_2[/math], directly from their definition and verify that [math]g(0) = 1[/math], [math]g'(0) = \mu_1[/math], and [math]g''(0) = \mu_2[/math].