exercise:Ea798f271e: 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 normally distributed on <math>(-\infty,+\infty)</math> with mean 0 and variance 1. Using the normal table provided in Appendix A, or the program ''' NormalArea''', find values for the function <m...") |
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Let <math>X</math> be a continuous random variable normally distributed on <math>(-\infty,+\infty)</math> with mean 0 and variance 1. Using the normal | |||
distributed on <math>(-\infty,+\infty)</math> with mean 0 and variance 1. Using the normal | |||
table provided in Appendix A, or the program ''' NormalArea''', | table provided in Appendix A, or the program ''' NormalArea''', | ||
find values for the function <math>f(x) = P(|X| \geq x)</math> as <math>x</math> increases from | find values for the function <math>f(x) = P(|X| \geq x)</math> as <math>x</math> increases from | ||
Latest revision as of 23:50, 14 June 2024
Let [math]X[/math] be a continuous random variable normally distributed on [math](-\infty,+\infty)[/math] with mean 0 and variance 1. Using the normal table provided in Appendix A, or the program NormalArea, find values for the function [math]f(x) = P(|X| \geq x)[/math] as [math]x[/math] increases from 0 to 4.0 in steps of .25. Note that for [math]x \geq 0[/math] the table gives [math] NA(0,x) = P(0 \leq X \leq x)[/math] and thus [math]P(|X| \geq x) = 2(.5 - NA(0,x)[/math]. Plot by hand the graph of [math]f(x)[/math] using these values, and the graph of the Chebyshev function [math]g(x) = 1/x^2[/math], and compare (see Exercise Exercise).