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9.9 Zeros on a Roulette Wheel: We now wish to make a more sophisticated estimate of the number of zeros on a roulette wheel without looking at the wheel. We will do so with Bayesian inference. 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. We assume that the number of zeros is one of {0, 1, 2, 3}. We assume that these cases have prior probability {0.1,0.2, 0.4, 0.3}. (a) Write n for the event that, in a single spin of the wheel, an odd/even bet will not be paid (equivalently, the ball lands in one of the zeros). Write z for the number of zeros in the wheel. What is P(n|z) for each of the possible values of z (i.e. each of (0, 1, 2, 3})? (b) Under what circumstances is P(z = 0|observations) NOT 0? (c) You observe 36 independent spins of the same wheel. A zero comes up in 2 of these spins. What is P(z|observations)?

9.9 Zeros on a Roulette Wheel: We now wish to make a more sophisticated estimate of the number of zeros on a roulette wheel without looking at the wheel. We will do so with Bayesian inference. 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. We assume that the number of zeros is one of {0, 1, 2, 3}. We assume that these cases have prior probability {0.1,0.2, 0.4, 0.3}. (a) Write n for the event that, in a single spin of the wheel, an odd/even bet will not be paid (equivalently, the ball lands in one of the zeros). Write z for the number of zeros in the wheel. What is P(n|z) for each of the possible values of z (i.e. each of (0, 1, 2, 3})? (b) Under what circumstances is P(z = 0|observations) NOT 0? (c) You observe 36 independent spins of the same wheel. A zero comes up in 2 of these spins. What is P(z|observations)?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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For part (b), the question is: What does "P (z = 0|observations) is NOT 0" imply?

9.9 Zeros on a Roulette Wheel: We now wish to make a more sophisticated estimate of the number of zeros on a roulette wheel without looking at the wheel. We will do so with Bayesian inference. 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. We assume that the number of zeros is one of {0, 1, 2, 3}. We assume that these cases have prior probability {0.1,0.2, 0.4, 0.3}. (a) Write n for the event that, in a single spin of the wheel, an odd/even bet will not be paid (equivalently, the ball lands in one of the zeros). Write z for the number of zeros in the wheel. What is P(n|z) for each of the possible values of z (i.e. each of (0, 1, 2, 3})? (b) Under what circumstances is P(z = 0|observations) NOT 0? (c) You observe 36 independent spins of the same wheel. A zero comes up in 2 of these spins. What is P(z|observations)?
Transcribed Image Text:9.9 Zeros on a Roulette Wheel: We now wish to make a more sophisticated estimate of the number of zeros on a roulette wheel without looking at the wheel. We will do so with Bayesian inference. 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. We assume that the number of zeros is one of {0, 1, 2, 3}. We assume that these cases have prior probability {0.1,0.2, 0.4, 0.3}. (a) Write n for the event that, in a single spin of the wheel, an odd/even bet will not be paid (equivalently, the ball lands in one of the zeros). Write z for the number of zeros in the wheel. What is P(n|z) for each of the possible values of z (i.e. each of (0, 1, 2, 3})? (b) Under what circumstances is P(z = 0|observations) NOT 0? (c) You observe 36 independent spins of the same wheel. A zero comes up in 2 of these spins. What is P(z|observations)?
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