[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]

In Exercise Exercise, the probability distribution is

completely determined by its first two moments. Show that this is always true for any probability distribution on [math]\{0,1,2\}[/math]. Hint: Given [math]\mu_1[/math] and [math]\mu_2[/math], find [math]h(z)[/math] as in Exercise Exercise and use [math]h(z)[/math] to determine [math]p[/math].