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]

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'[Notes 1] 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

  1. J. Galambos, Introductory Probability Theory (New York: Marcel Dekker, 1984), p. 159.