Question

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

Answer 1

Answer:

$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:

$A = E(X^{2})$ = (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.