Revision as of 03:22, 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> Let <math>X</math> be a random variable with density function <math>f_X</math>. The ''mode'' of <math>X</math> is the value <math>M</math> for which <math>f(M)</math> is maximum. Then values of <math>X</math> near <math>M</math> are most likely...")
BBy Bot
Jun 09'24
Exercise
[math]
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Let [math]X[/math] be a random variable with density function [math]f_X[/math].
The mode of [math]X[/math] is the value [math]M[/math] for which [math]f(M)[/math] is maximum. Then values of [math]X[/math] near [math]M[/math] are most likely to occur. Find [math]M[/math] if [math]X[/math] is distributed normally or exponentially, as in Exercise Exercise. What happens if [math]X[/math] is distributed uniformly?