[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]

Suppose we are observing a process such that the time

between occurrences is exponentially distributed with [math]\lambda = 1/30[/math] (i.e., the average time between occurrences is 30 minutes). Suppose that the process starts at a certain time and we start observing the process 3 hours later. Write a program to simulate this process. Let [math]T[/math] denote the length of time that we have to wait, after we start our observation, for an occurrence. Have your program keep track of [math]T[/math]. What is an estimate for the average value of [math]T[/math]?