# i am stuck on this problem Problem 6 (St Petersburg Paradox). Suppose you have the opportunity to play the following game. You ﬂip a fair coin, and if it comes up heads on the ﬁrst ﬂip, then you win \$1. If not, then you ﬂip again. 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, on the fourth \$8, and so on. That is, each time you get tails, you ﬂip again and your prize doubles, and you get paid the ﬁrst time you ﬂip heads.a) How much should you be willing to pay to play this amazing game? In other words, compute the expected payout from playing this game.For Part A, would the E(winning)= infinity?b) Now suppose the casino (or wherever you’re playing this game) has a limited bankroll of \$2n. So, if you get tails n times in a row, then the game is over automatically and you are paid \$2n. Now what is the expected payout? How much should you be willing to pay to play the game if n = 10? For Part B, would it be the same answer as Part A?

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i am stuck on this problem

Problem 6 (St Petersburg Paradox). Suppose you have the opportunity to play the following game. You ﬂip a fair coin, and if it comes up heads on the ﬁrst ﬂip, then you win \$1. If not, then you ﬂip again. 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, on the fourth \$8, and so on. That is, each time you get tails, you ﬂip again and your prize doubles, and you get paid the ﬁrst time you ﬂip heads.
a) How much should you be willing to pay to play this amazing game? In other words, compute the expected payout from playing this game.

For Part A, would the E(winning)= infinity?

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

For Part B, would it be the same answer as Part A?

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Step 1

As per the question,  Table is drawn. On First head you get 1 dollar, on second head you get the 2 dollar and on 3 you get 4 and so on.

Step 2

Expected payout is given by

Step 3

b)

Now here we have given n=10

Let n denotes the no of t...

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