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(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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(Lamperti<ref group="Notes" >Private communication.</ref>) | |||
Let <math>X</math> be a non-negative random | 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 | 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>. | <ul style="list-style-type:lower-alpha"><li> <math>E(X) = 20</math>. | ||
</li> | </li> | ||
<li> <math>E(X) = 20</math> and <math>V(X) = 25</math>. | <li> <math>E(X) = 20</math> and <math>V(X) = 25</math>. | ||
Latest revision as of 23:52, 14 June 2024
(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