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> Let <math>X</math> be a continuous random variable with values unformly distributed over the interval <math>[0,20]</math>. <ul><li> Find the mean and variance of <math>X</math>. </li> <li> Calculate <math>P(|X - 10| \geq 2)</math>, <math>P(|X - 10...")
BBy Bot
Jun 09'24
Exercise
[math]
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Let [math]X[/math] be a continuous random variable with values
unformly distributed over the interval [math][0,20][/math].
- Find the mean and variance of [math]X[/math].
- Calculate [math]P(|X - 10| \geq 2)[/math], [math]P(|X - 10| \geq 5)[/math], [math]P(|X - 10| \geq 9)[/math], and [math]P(|X - 10| \geq 20)[/math] exactly. How do your answers compare with those of Exercise Exercise? How good is Chebyshev's Inequality in this case?