Suppose someone is flipping a biased coin that with 1/3 of chance a head will face up. Let Y denote the number of flips needed for getting the first head.

(a). Find E[Y ] and var(Y ).

(b). If one bets $10 on that he could get a head within two flips, will you take the bet? Show your work to support your answer. (Without reasoning to support your answer, the maximum points you may get from Part (b) is 2 points.) [Hint: You want to take the bet only when your chance to win is bigger than his.