Consider a simple gambling game. Each time you bet $10. If you lose (with probability 1 - p), you lose the $10 you bet; if you win(with probability p), you get back your $10 and win extra $10 dollars. The games are assumed to be independent from one time to another. Suppose you play the game repeatedly. Define a random variable N to be the number of games until your first winning.

(a) Give the distribution of N.

(b) Let L be the total amount of dollars you have lost until your first winning. Write L as a function of N.

(c) Find the the expected loss E(L) until your first winning.