Suppose that a person wins a game of chance with probability 0.40, and loses otherwise. If he wins, he earns 5 dollars, and if he loses, then he loses 4 dollars.
a. What is his expected gain or loss?
b. What is the variance of his gain or loss?
c. Find constants a, b such that if X = 0 when he loses and X = 1 when he wins, then Y = aX + b is his earnings. Verify your results above by finding E(Y) and Var(Y) with this method.