Suppose we play the following game based on tosses of a fair coin. You pay me $10, and I agree to pay you $n2 if heads comes up rst on the nth toss. If we play this game repeatedly, how much money do you expect to win or lose per game over the long run

$4

Explanation:

A geometric distribution is commonly known as a probability distribution that is used for the total number of Bernoulli trials computed till there is a successful trial. Therefore:

If X is the toss with the first head, then, it is a geometric distribution with p = 0.5. The payable amount (A) will be:

= (1+0.5)/(0.5)^2 = 1.5/0.25 = 6

If $10 is used to play the game, the loss will be 10-6 = $4 per game.

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