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Homework 7 solutions

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Question 1 Taxicab Example of Bayesian Thinking • Suppose there has been a hit-and-run accident. A person was struck by a taxicab last night. There are two cab companies in town, Blue Cab and Gre ... en Cab. The only witness, who was some distance away, believes it was a blue vehicle he saw cause the accident. Which cab company is guilty? • Green Cab Company had 90 cabs on the street at the time of the accident, while Blue Cab Company had only 10 cabs out. • Given the lighting and visibility at the time of the accident, a person could correctly distinguish a blue from a green cab about 80% of the time, at the distance the witness said he was from the accident. (One can always tell if it was a taxicab or not.) What is the probability that the cab was from Blue Cab? (Answer: approximately 30%.) G − green cab B − blue cab T − Testimony is Blue cab P(G) = 0:9; P(B) = 0:1 P(TjB) = 0:8 P(Tj:B) = P(TjG) = 0:2 P(BjT) = P(TjB)P(B) P(T) = P(TjB)P(B) P(TjB)P(B) + P(Tj:B)P(:B) = 0:8 · 0:1 0:8 · 0:1 + 0:2 · (1 − 0:1) ≈ 0:308 Question 2 Question 1 We believe that the relation between the Boolean variables A, B, C can be approximated by: A ! B and B ! C. A careful examination of the conditional probabilities gives: Prob(A) = 0:2; Prob(B j A = 0) = 0:7; Prob(B j A = 1) = 0:8 Prob(C j B = 0) = 0:5; Prob(C j B = 1) = 0:6 Produce a graphic representation of this as a Bayesian network [Show More]

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