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60A99-MarkovsInequality.tex
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60A99-MarkovsInequality.tex
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\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{MarkovsInequality}
\pmcreated{2013-03-22 12:34:08}
\pmmodified{2013-03-22 12:34:08}
\pmowner{Andrea Ambrosio}{7332}
\pmmodifier{Andrea Ambrosio}{7332}
\pmtitle{Markov's inequality}
\pmrecord{6}{32817}
\pmprivacy{1}
\pmauthor{Andrea Ambrosio}{7332}
\pmtype{Theorem}
\pmcomment{trigger rebuild}
\pmclassification{msc}{60A99}
\pmsynonym{Markoff's inequality}{MarkovsInequality}
\pmrelated{ChebyshevsInequality2}
\pmrelated{KolmogorovsInequality}
\pmrelated{KolmogorovsMartingaleInequality}
\pmrelated{ReverseMarkovInequality}
\endmetadata
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%%%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here
\begin{document}
For a non-negative random variable $X$ and a standard of accuracy $d > 0$, Markov's inequality \PMlinkescapetext{states} that $P[X \ge d] \le \frac{1}{d} E[X]$.
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\end{document}