[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]

Find the maximum possible value for [math]p(1 - p)[/math] if [math]0 \lt p \lt 1[/math]. Using this result and Exercise Exercise, show that the estimate

[[math]] P\left( \left| \frac {S_n}n - p \right| \geq \epsilon \right) \leq \frac 1{4n\epsilon^2} [[/math]]

is valid for any [math]p[/math].