Revision as of 03:21, 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> Suppose we know a random variable <math>Y</math> as a function of the uniform random variable <math>U</math>: <math>Y = \phi(U)</math>, and suppose we have calculated the cumulative distribution function <math>F_Y(y)</math> and thence the density...")
BBy Bot
Jun 09'24
Exercise
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Suppose we know a random variable [math]Y[/math] as a function of the
uniform random variable [math]U[/math]: [math]Y = \phi(U)[/math], and suppose we have calculated the cumulative distribution function [math]F_Y(y)[/math] and thence the density [math]f_Y(y)[/math]. How can we check whether our answer is correct? An easy simulation provides the answer: Make a bar graph of [math]Y = \phi(\mbox{[/math]rnd[math]})[/math] and compare the result with the graph of [math]f_Y(y)[/math]. These graphs should look similar. Check your answers to Exercises \ref{exer 5.2.1} and Exercise by this method.