[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]

A die is rolled until the first time that a six

turns up. We shall see that the probability that this occurs on the [math]n[/math]th roll is [math](5/6)^{n-1}\cdot(1/6)[/math]. Using this fact, describe the appropriate infinite sample space and distribution function for the experiment of rolling a die until a six turns up for the first time. Verify that for your distribution function [math]\sum_{\omega} m(\omega) = 1[/math].