[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]

An insurance company assumes that the time between claims from

each of its homeowners' policies is exponentially distributed with mean [math]\mu[/math]. It would like to estimate [math]\mu[/math] by averaging the times for a number of policies, but this is not very practical since the time between claims is about 30 years. At Galambos' suggestion the company puts its customers in groups of 50 and observes the time of the first claim within each group. Show that this provides a practical way to estimate the value of [math]\mu[/math].

Notes