exercise:218f709383: Difference between revisions
From Stochiki
(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...") |
No edit summary |
||
| Line 1: | Line 1: | ||
(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 independently and uniformly from <math>[0, 1]</math>. The game ends the first time that <math>Y_i~ > ~X</math>. You are then paid <math>(i-1)</math> dollars. What is a fair entrance fee for this game? | |||
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~ > ~X</math>. You are then paid <math>(i-1)</math> dollars. What is | |||
a fair entrance fee for this game? | |||
'''Notes''' | '''Notes''' | ||
{{Reflist|group=Notes}} | {{Reflist|group=Notes}} | ||
Latest revision as of 21:54, 14 June 2024
(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