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Bayes Theorem and Standardization

# Bayes Theorem and Standardization - Help Session II...

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Help Session II: Practice Problems 21.16 To save on expenses, Rona and Jerry agreed to carpool for traveling to and from work. Rona preferred to use the somewhat longer and more consistent Queen City Avenue. Although Jerry preferred the quicker expressway, he agreed with Rona that they should take the Queen City Avenue if the expressway had a traffic jam. The following payoff table provides the one-way estimate in minutes for traveling to and from work. Decision/State of Nature Expressway open (s1) Expressway jammed (s2) Queen City Avenue 30 30 Expressway 25 45 Based on the experience with traffic problems, Rona and Jerry agreed on a 0.15 probability that the expressway would be jammed. In addition, they agreed that weather seemed to affect the traffic conditions on the expressway. Let C = Clear, O = overcast, R = rain The following conditional probabilities apply. P(C|s1) = 0.8 , P (O|s1) = 0.2 P(C|s2) = 0.1, P(O|s2) = 0.3 a) Use Bayes’ theorem for probability revision to compute the probability of each weather condition and the conditional probability of the expressway open or jammed given each weather condition. b) Show the decision tree for the problem c) What is the optimal decision strategy, and what is the expected travel time?

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5.58 Many companies use a quality control technique called acceptance sampling to monitor incoming shipments of parts, raw materials, and so on. In the electronics industry, component parts are commonly shipped from suppliers in large lots. Inspection of a sample of
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