[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] by any random variable which takes on values 0, 1, 2,

\dots, [math]n[/math] and has [math]E(X) = V(X) = 1[/math]. Show that, for any positive integer [math]k[/math],

[[math]] P(X \geq k + 1) \leq \frac 1{k^2}\ . [[/math]]