[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]S_n[/math] be the number of successes in [math]n[/math] Bernoulli

trials with probability [math]p[/math] for success on each trial. Show, using Chebyshev's Inequality, that for any [math]\epsilon \gt 0[/math]

[[math]] P\left( \left| \frac {S_n}n - p \right| \geq \epsilon \right) \leq \frac {p(1 - p)}{n\epsilon^2}\ . [[/math]]