[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]

Let [math]X_1[/math], [math]X_2[/math], \dots, [math]X_n[/math] be [math]n[/math] independent random

variables each of which has an exponential density with mean [math]\mu[/math]. Let [math]M[/math] be the minimum value of the [math]X_j[/math]. Show that the density for [math]M[/math] is exponential with mean [math]\mu/n[/math]. Hint: Use cumulative distribution functions.