Revision as of 03:36, 9 June 2024 by Bot (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> Suppose that a gambler starts with a stake of 0 dollars. <ul><li> Show that the probability that her stake never reaches <math>M</math> before returning to 0 equals <math>1 - p(1 - q_1)</math>. </li> <li> Show that the probability that her stake...")
BBy Bot
Jun 09'24
Exercise
[math]
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Suppose that a gambler starts with a stake of 0 dollars.
- Show that the probability that her stake never reaches [math]M[/math] before returning to 0 equals [math]1 - p(1 - q_1)[/math].
- Show that the probability that her stake reaches the value [math]M[/math] exactly [math]k[/math] times before returning to 0 equals [math]p(1-q_1)(1 - qq_{M-1})^{k-1}(qq_{M-1})[/math]. Hint: Use Exercise Exercise.