exercise:Db0a33eb2b: 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> 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...") |
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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{$rnd$})</math> and compare the result with the graph of <math>f_Y(y)</math>. These graphs should look similar. Check your answers to [[exercise:7fa69eccf0|Exercise]] and [[exercise:D1cdb3fbcc |Exercise]] by this method. | |||
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>f_Y(y)</math>. These graphs should look similar. Check your answers to | |||
Latest revision as of 00:55, 14 June 2024
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{$rnd$})[/math] and compare the result with the graph of [math]f_Y(y)[/math]. These graphs should look similar. Check your answers to Exercise and Exercise by this method.