A player tosses two fair coins, he wins Rs. 5 if two heads appear, Rs. 3 if one head appears and Rs. 2 if no head appears, then the variance of the winning amount is

Step-by-step solution

Let X be the random variable denoting the winning amount. The possible outcomes for the number of heads when tossing two fair coins are 0, 1, and 2 . The probabilities and corresponding winning amounts are: P(X = 5) = P(2 heads ) = 1 4 P(X = 3) = P(1 head ) = 1 2 P(X = 2) = P(0 heads ) = 1 4 The expected value E(X) is given by: E(X) = X P(X) = 5 1 4 + 3 1 2 + 2 1 4 = 5 4 + 6 4 + 2 4 = 13 4 The expected value of X^2 , E(X^2) is: E(X^2) = X^2 P(X) = 25 1 4 + 9 1 2 + 4 1 4 = 25 4 + 18 4 + 4 4 = 47 4 The variance of X