A player tosses 2 fair coins. He wins Rs. 5 if 2 heads appear, Rs. 2 If 1 head appear and Rs. 1 if no head appears, then variance of his winning amount is

Step-by-step solution

When player tosses 2 fair coins then S = H T , T H , T T , H H Let X be a random variable that denotes the amount received by the player. Then, X can take value 5, 2 and 1. Now, P X = 5 = 1 4 , P X = 2 = 2 4 = 1 2 and P X = 1 = 1 4 Thus, the probability distribution of X is X 5 2 1 ¯ P X 1 4 1 2 1 4 - ∴ Variance of X = ∑ X 2 P X - ∑ X P X 2 Now ∑ X P X = 5 × 1 4 + 2 × 1 2 + 1 × 1 4 = 5 4 + 4 4 + 1 4 = 10 4 = 5 2 ∴ Variance of X = ∑ X 2 P X - ∑ X P X 2 = 25 × 1 4 + 4 × 1 2 + 1 × 1 4 - 5 2 2 = 25 + 8 + 1 4 - 25 4 = 9