Revision as of 02:21, 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 cumulative distribution function <math>F</math> strictly increasing on the range of <math>X</math>. Let <math>Y = F(X)</math>. Show that <math>Y</math> is uniformly distributed in the interval <math>[...")
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]
Let [math]X[/math] be a random variable with cumulative distribution function [math]F[/math]
strictly increasing on the range of [math]X[/math]. Let [math]Y = F(X)[/math]. Show that [math]Y[/math] is uniformly distributed in the interval [math][0,1][/math]. (The formula [math]X = F^{-1}(Y)[/math] then tells us how to construct [math]X[/math] from a uniform random variable [math]Y[/math].)