exercise:34d20a6468: Difference between revisions
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(Created page with "<div class="d-none"><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></div> 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...") |
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A die is rolled until the first time that a six turns up. We shall | |||
turns up. We shall | |||
see that the probability that this occurs on the <math>n</math>th roll is | 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 | <math>(5/6)^{n-1}\cdot(1/6)</math>. Using this fact, describe the appropriate infinite | ||
Latest revision as of 22:08, 12 June 2024
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].