Revision as of 02:28, 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> 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>...")
BBy Bot
Jun 09'24
Exercise
[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]
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.