Revision as of 03:26, 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 that <math>R^2 = X^2 + Y^2</math>. Find <math>f_{R^2}</math> and <math>f_R</math> if <math display="block"> f_X(x) = f_Y(x) = \left \{ \begin{array}{ll} 1/2, & \mbox{if $-1 \leq x \leq 1,$} \\ 0, &...")
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]
Suppose that [math]R^2 = X^2 + Y^2[/math]. Find [math]f_{R^2}[/math] and [math]f_R[/math] if
[[math]]
f_X(x) = f_Y(x) = \left \{ \begin{array}{ll}
1/2, & \mbox{if $-1 \leq x \leq 1,$} \\
0, & \mbox{otherwise.}
\end{array}
\right.
[[/math]]