Revision as of 02:26, 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> (from Hamming<ref group="Notes" >ibid., pg. 205.</ref>) A game is played as follows: A random number <math>X</math> is chosen uniformly from <math>[0, 1]</math>. Then a sequence <math>Y_1, Y_2, \ldots</math> of random numbers is chosen independ...")
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Jun 09'24

Exercise

[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]

(from Hamming[Notes 1]) A game is

played as follows: A random number [math]X[/math] is chosen uniformly from [math][0, 1][/math]. Then a sequence [math]Y_1, Y_2, \ldots[/math] of random numbers is chosen independently and uniformly from [math][0, 1][/math]. The game ends the first time that [math]Y_i~ \gt ~X[/math]. You are then paid [math](i-1)[/math] dollars. What is a fair entrance fee for this game?

Notes

  1. ibid., pg. 205.