Question

9.4 Fitting a Geometric Model: You wish to determine the number of zeros on a roulette 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 r₁ odd/even bets being paid
before you see a bet not being paid; in the second, r₂ ; and in the third, r₃ . What is the maximum likelihood estimate of
the number of slots on the wheel?

Answer 1

To fit a geometric model to the given problem we first assume that the proportion of zero slots on the wheel is "p" , the parameter of the distribution.We'll find the MLE of p first then by using the invarianve property of MLE we determine the MLE of the no of slots on the wheel S=36/(1-p).The explanations are given in the images...