exercise:352bb007a7: 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> You are offered the following game. A fair coin will be tossed until the first time it comes up heads. If this occurs on the <math>j</math>th toss you are paid <math>2^j</math> dollars. You are sure to win at least 2 dollars so you should be wi...") |
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You are offered the following game. A fair coin will be tossed until the | |||
tossed until the | |||
first time it comes up heads. If this occurs on the <math>j</math>th toss you are paid | first time it comes up heads. If this occurs on the <math>j</math>th toss you are paid | ||
<math>2^j</math> dollars. You are sure to win at least 2 dollars so you should be | <math>2^j</math> dollars. You are sure to win at least 2 dollars so you should be | ||
Latest revision as of 20:27, 12 June 2024
You are offered the following game. A fair coin will be tossed until the first time it comes up heads. If this occurs on the [math]j[/math]th toss you are paid [math]2^j[/math] dollars. You are sure to win at least 2 dollars so you should be willing to pay to play this game---but how much? Few people would pay as much as 10 dollars to play this game. See if you can decide, by simulation, a reasonable amount that you would be willing to pay, per game, if you will be allowed to make a large number of plays of the game. Does the amount that you would be willing to pay per game depend upon the number of plays that you will be allowed?