Continue to use the scenario from the previous problem. As before, let X denote the number of games that he must play until (and including) his first win. Assume that, if he wins, he earns 5 dollars, and if he loses, then he loses 4 dollars. (Also assume that he is allowed to borrow money, i.e., having a negative amount of money is not a problem here.)
a. Find a formula for his gain or loss, in terms of X, i.e., if Y denotes his gain or loss in dollars, write Y in terms of X.
b. What is his expected gain or loss (altogether) during the X games, i.e., I what is E(Y)?
c. What is the variance of his gain or loss (altogether) during the X games, i.e., what is Var(Y)?