Revision as of 02:27, 9 June 2024 by Bot (Created page with "<div class="d-none"><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></div> 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 display="block"> P(X \geq k + 1) \leq \frac 1{k^2}\ ....")
BBy Bot
Jun 09'24
Exercise
[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]]