Revision as of 03:28, 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> (Lamperti<ref group="Notes" >Private communication.</ref>) Let <math>X</math> be a non-negative random variable. What is the best upper bound you can give for <math>P(X \geq a)</math> if you know <ul><li> <math>E(X) = 20</math>. </li> <li> <math>...")
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Jun 09'24
Exercise
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(Lamperti[Notes 1])
Let [math]X[/math] be a non-negative random variable. What is the best upper bound you can give for [math]P(X \geq a)[/math] if you know
- [math]E(X) = 20[/math].
- [math]E(X) = 20[/math] and [math]V(X) = 25[/math].
- [math]E(X) = 20[/math], [math]V(X) = 25[/math], and [math]X[/math] is symmetric about its mean.
Notes