exercise:A5b5ddac8d: Difference between revisions
From Stochiki
(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> A die is rolled twice. Let <math>X</math> denote the sum of the two numbers that turn up, and <math>Y</math> the difference of the numbers (specifically, the number on the first roll minus the number on the second). Show that <math>E(XY) = E(X)E...") |
No edit summary |
||
| Line 5: | Line 5: | ||
\newcommand{\secstoprocess}{\all} | \newcommand{\secstoprocess}{\all} | ||
\newcommand{\NA}{{\rm NA}} | \newcommand{\NA}{{\rm NA}} | ||
\newcommand{\mathds}{\mathbb}</math></div> A die is rolled twice. Let <math>X</math> denote the sum of the two | \newcommand{\mathds}{\mathbb}</math></div> A die is rolled twice. Let <math>X</math> denote the sum of the two numbers that turn up, and <math>Y</math> the difference of the numbers (specifically, the number on the first roll minus the number on the second). Show that <math>E(XY) = E(X)E(Y)</math>. Are <math>X</math> and <math>Y</math> independent? | ||
numbers that turn up, and <math>Y</math> the difference of the numbers (specifically, the number | |||
on the first roll minus the number on the second). Show that <math>E(XY) = E(X)E(Y)</math>. Are | |||
<math>X</math> and <math>Y</math> independent? | |||
Latest revision as of 01:46, 16 June 2024
[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]
A die is rolled twice. Let [math]X[/math] denote the sum of the two numbers that turn up, and [math]Y[/math] the difference of the numbers (specifically, the number on the first roll minus the number on the second). Show that [math]E(XY) = E(X)E(Y)[/math]. Are [math]X[/math] and [math]Y[/math] independent?