Consider a game that pays 2ⁿ cents if the first tail is on the n^th toss of a fair-headed coin.Determine the expected value of this game.

Question

Quizplus · Accepted Answer

The expected value is calculated by summing the products of each outcome's value and its probability. The probability of the first tail occurring on the n-th toss is (1/2)^n, and the payout is 2^n cents. The expected value is the sum of (2^n * (1/2)^n) for n = 1 to infinity, which simplifies to an infinite series that diverges, resulting in an infinite expected value.

Consider a Game That Pays 2n Cents If the First

Consider a Game That Pays 2ⁿ Cents If the First