exercise:442c66dc7c: 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 exponentially distributed over <math>[0,\infty)</math> with parameter <math>\lambda = 0.1</math>. <ul><li> Find the mean and variance of <math>X</math>. </li> <li> Using Chebyshev's In...") |
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Let <math>X</math> be a continuous random variable with values exponentially distributed over <math>[0,\infty)</math> with parameter <math>\lambda = 0.1</math>. | |||
<ul style="list-style-type:lower-alpha"><li> Find the mean and variance of <math>X</math>. | |||
distributed over <math>[0,\infty)</math> with parameter <math>\lambda = 0.1</math>. | |||
<ul><li> Find the mean and variance of <math>X</math>. | |||
</li> | </li> | ||
<li> Using Chebyshev's Inequality, find an upper bound for the following | <li> Using Chebyshev's Inequality, find an upper bound for the following | ||
Latest revision as of 22:47, 14 June 2024
Let [math]X[/math] be a continuous random variable with values exponentially distributed over [math][0,\infty)[/math] with parameter [math]\lambda = 0.1[/math].
- Find the mean and variance of [math]X[/math].
- Using Chebyshev's Inequality, find an upper bound for the following probabilities: [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].
- Calculate these probabilities exactly, and compare with the bounds in (b).