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. Assume that he plays ten games independently. Let X denote the number of games that he wins. (His gain or loss is 5X + (-4)(10 - X) = 9X - 40, since he loses 10 - X games.)
a. What is his expected gain or loss (altogether) during the ten games?
b. What is the variance of his gain or loss (altogether) during the ten games?
c. What is the probability that he wins $32 or more during the ten games? i