Question

Problem 2 - Bayesian Inference Nisqually, Inc. sells books A,B,C on line. Each customer buys 0 or 1 copy of each title. a. Mrs. Independence Day, the company's data mining expert, makes the assumptions that: i) a customer decides to buy a book independently of what other books (s)he buys and independently of other customers. ii) all customers buy according to the same joint probability distribution PABC = PAPeP. with PA(1)0.6, PB(1) 0.3, Pc1) 0.4. For example, the probability that a customer buys A and B but not C is PABC(1,1,0) 0.6 x 0.3 x (1- 0.4) Compute the probability that a customer buys all three books under PABC b. Mr. Mean Variance, her aide, insists that Mrs. Day's model is not correct. He assumes that ii) all customers buy according to the same probability distribution; but iii) Book C is bought independently from A, B but A, B are not independent of each other. С А. B A羊B Denote Mr. Variance's model by PABC PABPC with Pc(1) 0.4, and PAB : For example, PABC (1,0,0) 0.5 x (1 0.4). Compute the probability that a B0 0.2 0.5 1 0.2 0.1 customer buys all three books under P. c. Al Bayes, the guy who fills out the orders, notices that in fact women buy according to model P while men buy according to model P. The next customer, Robin Hood, has ordered books A, B but not C. Using P and P from above, determine if the likelihood that Robin Hood is a man is higher than the likelihood that (s)he's a woman

Answer 1

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