[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]

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]]