exercise:40407c4554: 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> If <math>X</math> is normally distributed, with mean <math>\mu</math> and variance <math>\sigma^2</math>, find an upper bound for the following probabilities, using Chebyshev's Inequality. <ul><li> <math>P(|X - \mu| \geq \sigma)</math>. </li> <li>...") |
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If <math>X</math> is normally distributed, with mean <math>\mu</math> and | |||
variance <math>\sigma^2</math>, find an upper bound for the following probabilities, using Chebyshev's | variance <math>\sigma^2</math>, find an upper bound for the following probabilities, using Chebyshev's | ||
Inequality. | Inequality. | ||
<ul><li> <math>P(|X - \mu| \geq \sigma)</math>. | <ul style="list-style-type:lower-alpha"><li> <math>P(|X - \mu| \geq \sigma)</math>. | ||
</li> | </li> | ||
<li> <math>P(|X - \mu| \geq 2\sigma)</math>. | <li> <math>P(|X - \mu| \geq 2\sigma)</math>. | ||
Latest revision as of 23:48, 14 June 2024
If [math]X[/math] is normally distributed, with mean [math]\mu[/math] and variance [math]\sigma^2[/math], find an upper bound for the following probabilities, using Chebyshev's Inequality.
- [math]P(|X - \mu| \geq \sigma)[/math].
- [math]P(|X - \mu| \geq 2\sigma)[/math].
- [math]P(|X - \mu| \geq 3\sigma)[/math].
- [math]P(|X - \mu| \geq 4\sigma)[/math].
Now find the exact value using the program NormalArea or the normal table in Appendix A, and compare.