[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]

Write a computer program to calculate the mean and variance

of a distribution which you specify as data. Use the program to compare the variances for the following densities, both having expected value 0:

[[math]] p_X = \pmatrix{ -2 & -1 & 0 & 1 & 2 \cr 3/11 & 2/11 & 1/11 & 2/11 & 3/11 \cr}\ ; [[/math]]

[[math]] p_Y = \pmatrix{ -2 & -1 & 0 & 1 & 2 \cr 1/11 & 2/11 & 5/11 & 2/11 & 1/11 \cr}\ . [[/math]]