[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]

If [math]X[/math] is a random variable with mean [math]\mu \ne 0[/math] and variance [math]\sigma^2[/math],

define the relative deviation [math]D[/math] of [math]X[/math] from its mean by

[[math]] D = \left| \frac {X - \mu}\mu \right|\ . [[/math]]

• Show that [math]P(D \geq a) \leq \sigma^2/(\mu^2a^2)[/math].
• If [math]X[/math] is the random variable of Exercise Exercise, find an upper bound for [math]P(D \geq .2)[/math], [math]P(D \geq .5)[/math], [math]P(D \geq .9)[/math], and [math]P(D \geq 2)[/math].