exercise:8d88473caa: 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> Let <math>X</math> and <math>Y</math> be independent random variables with uniform densities in <math>[0,1]</math>. Let <math>Z = X + Y</math> and <math>W = X - Y</math>. Find <ul><li> <math>\rho(X,Y)</math> (see Exercise exercise:0a82eb3e0d |...") |
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Let <math>X</math> and <math>Y</math> be independent random variables with uniform densities in <math>[0,1]</math>. Let <math>Z = X + Y</math> and <math>W = X - Y</math>. Find | |||
<ul style="list-style-type:lower-alpha"><li> <math>\rho(X,Y)</math> (see [[exercise:0a82eb3e0d |Exercise]]). | |||
densities in <math>[0,1]</math>. Let <math>Z = X + Y</math> and <math>W = X - Y</math>. Find | |||
<ul><li> <math>\rho(X,Y)</math> (see | |||
</li> | </li> | ||
<li> <math>\rho(X,Z)</math>. | <li> <math>\rho(X,Z)</math>. | ||
Latest revision as of 22:44, 14 June 2024
Let [math]X[/math] and [math]Y[/math] be independent random variables with uniform densities in [math][0,1][/math]. Let [math]Z = X + Y[/math] and [math]W = X - Y[/math]. Find
- [math]\rho(X,Y)[/math] (see Exercise).
- [math]\rho(X,Z)[/math].
- [math]\rho(Y,W)[/math].
- [math]\rho(Z,W)[/math].