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> (The next three problems come from Feller.<ref group="Notes" >W. Feller, op.\ cit., pg. 367.</ref>) As in the text, assume that <math>M</math> is a fixed positive integer. <ul><li> Show that if a gambler starts with an stake of 0 (and is allowed...")
BBy Bot
Jun 09'24
Exercise
[math]
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(The next three problems come from Feller.[Notes 1])
As in the text, assume that [math]M[/math] is a fixed positive integer.
- Show that if a gambler starts with an stake of 0 (and is allowed to have a negative amount of money), then the probability that her stake reaches the value of [math]M[/math] before it returns to 0 equals [math]p(1 - q_1)[/math].
- Show that if the gambler starts with a stake of [math]M[/math] then the probability that her stake reaches 0 before it returns to [math]M[/math] equals [math]qq_{M-1}[/math].
Notes