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  3. (st petersburg paradox). suppose you have the oppo

(St Petersburg Paradox). Suppose you have the opportunity to play the following game. You flip a...

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Basic Math

(St Petersburg Paradox). Suppose you have the opportunity toplay the following game. You flip a fair coin, and if it comes upheads on the first flip, then you win $1. If not, then you flipagain. If it comes up heads on the second flip, then you win $2,and if not you flip again. On the third flip, a heads pays $4, onthe fourth $8, and so on. That is, each time you get tails, youflip again and your prize doubles, and you get paid the first timeyou flip heads.

a) How much should you be willing to pay to play this amazinggame? In other words, compute the expected payout from playing thisgame.

b) Now suppose the casino (or wherever you’re playing this game)has a limited bankroll of $2^n. So, if you get tails n times in arow, then the game is over automatically and you are paid $2^n. Nowwhat is the expected payout? How much should you be willing to payto play the game if n = 10?

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