a Given that Ms Jones apply for both jobs, denote A as the...

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SEEM 4480 Decision Methodology and Applicatons Xuedong He, Fall 2017 Suggested Solution to Homework 3 1. (a) Given that Ms. Jones apply for both jobs, denote A as the event that Ms. Jones will be accepted for the first job and B as the event that she will be accepted for the second job. Denote P as the probability measure that represents Ms. Jones’ subjective belief. Then, we have P ( A ) = 0 . 7, P ( B ) = 0 . 5, and P ( B | A ) = 0 . 6. We want to compute P ( A B ). Denote ¯ B as the complement to B .
(b) If Ms. Jones applies the third job, she feels that the probability of getting the job is 0.7. If she applies the first two jobs, she feels that the probability of getting at least one of them is 0.78. Thus, she should apply for the first two jobs. 2. Denote N for normal and A for abnormal. Then, the diagram reveals that P ( x 1 = 1 | N ) = 0 . 2 , P ( x 1 = 0 | N ) = 0 . 8 , P ( x 2 = 2 | N, x 1 = 1) = 0 . 2 , P ( x 2 = 1 | N, x 1 = 1) = 0 . 3 , P ( x 2 = 0 | N, x 1 = 1) = 0 . 5 , P ( x 1 = 1 | A ) = 0 . 7 , P ( x 1 = 0 | A ) = 0 . 3 , P ( x 2 = 2 | A, x 1 = 1) = 0 . 7 , P ( x 2 = 1 | A, x 1 = 1) = 0 . 2 , P ( x 2 = 0 | A, x 1 = 1) = 0 . 1 .
(b) Following this rule, a normal is misclassified as an abnormal if and only if a normal is classified as 1 on measurement 1 and as 1 on measure 2. Thus, 1
SEEM 4480 Decision Methodology and Applicatons Xuedong He, Fall 2017

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