[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]X[/math] be a continuous random variable and define the

standardized version [math]X^*[/math] of [math]X[/math] by:

[[math]] X^* = \frac {X - \mu}\sigma\ . [[/math]]

• Show that [math]P(|X^*| \geq a) \leq 1/a^2[/math].
• If [math]X[/math] is the random variable of Exercise Exercise, find bounds for [math]P(|X^*| \geq 2)[/math], [math]P(|X^*| \geq 5)[/math], and [math]P(|X^*| \geq 9)[/math].