Revision as of 02:27, 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> Assume that <math>X_1</math> and <math>X_2</math> are independent random variables, each having an exponential density with parameter <math>\lambda</math>. Show that <math>Z = X_1 - X_2</math> has density <math display="block"> f_Z(z) = (1/2)\la...")
BBy Bot
Jun 09'24
Exercise
[math]
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Assume that [math]X_1[/math] and [math]X_2[/math] are independent random variables, each
having an exponential density with parameter [math]\lambda[/math]. Show that [math]Z = X_1 - X_2[/math] has density
[[math]]
f_Z(z) = (1/2)\lambda e^{-\lambda |z|}\ .
[[/math]]