exercise:B00c277b78: Difference between revisions
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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> 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...") |
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Let <math>X</math> be a continuous random variable with values | |||
unformly distributed over the interval <math>[0,20]</math>. | unformly distributed over the interval <math>[0,20]</math>. | ||
<ul><li> Find the mean and variance of <math>X</math>. | <ul style="list-style-type:lower-alpha"><li> Find the mean and variance of <math>X</math>. | ||
</li> | </li> | ||
<li> Calculate <math>P(|X - 10| \geq 2)</math>, <math>P(|X - 10| \geq 5)</math>, <math>P(|X - 10| \geq | <li> 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 | 9)</math>, and <math>P(|X - 10| \geq 20)</math> exactly. How do your answers compare with those | ||
of | of [[exercise:63ec956b0e |Exercise]]? How good is Chebyshev's Inequality in this case? | ||
</li> | </li> | ||
</ul> | </ul> | ||
Latest revision as of 22:43, 14 June 2024
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? How good is Chebyshev's Inequality in this case?