You wish to determine the number of zeros on a rouletle wheel without looking at the wheel. You will do so with a geometric model. Recall that when a ball on a roulette wheel falls into a non-zero slot, odd/even bets are paid; when it falls into a zero slot, they are not paid. There are 36 non-zero slots on the wheel. (a) Assume you observe a total of r odd/even bets being paid before you see a bet not being paid. What is the maximum likelihood estimate of the number of slots on the wheel?
(b) How reliable is this estimate? Why?
(c) You decide to watch the wheel k times to make an estimate. In the first experiment, you see ri odd/even bets being paid before you see a bet not being paid; in the second, rz; and in the third, r3. What is the maximum likelihood estimate of the number of slots on the wheel?