A fair coin is flipped.You will be paid $1 when it is heads and penalized $1 otherwise.What is the variance of the payoffs?

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Quizplus · Accepted Answer

The variance of the payoffs for a fair coin flip, where the payoff is $1 for heads and -$1 for tails, is calculated using the formula for variance of a discrete random variable. The expected value (E[X]) is 0, since there's a 50% chance of winning $1 and a 50% chance of losing $1. The variance is calculated as E[X^2] - (E[X])^2. Here, E[X^2] = (0.5 * 1^2) + (0.5 * (-1)^2) = 0.5 + 0.5 = 1, and (E[X])^2 = 0^2 = 0. Therefore, the variance is 1 - 0 = 1.

A Fair Coin Is Flipped