PreWorkSolution

# PreWorkSolution - Dr Edwin Romeijn Prework Problem Set...

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Dr. Edwin Romeijn ESI 6321 Applied Probability Methods in Engineering Prework Problem Set - Solutions Class of 2009 - 1 - ESI 6321 APPLIED PROBABILITY METHODS IN ENGINEERING OUTREACH ENGINEERING MANAGEMENT Class of 2009 PREWORK PROBLEM SET - SOLUTIONS Exercise 2.1 (a) P(X 5) = P(1,4) + P(2,3) + P(2,4) + P(3,2) + P(3,3) + P(3,4) + P(4,1) + P(4,2) + P(4,3) + P(4,4) = 10/16. (b) P(X 5 | First is 3) = P(X 5 and First is 3)/P(First is 3) = (3/16)/(1/4)=3/4. (c) P(X 5 | At least 3 in one die) = P(X 5 and At least 3 in one die)/P(At least 3 in one die) = (5/16)/(7/16)=5/7. Exercise 2.5 (a) P(Sunny on Wednesday) = P(Sunny on Tuesday and sunny on Wednesday) + P(Cloudy on Tuesday and sunny on Wednesday) = (0.30)x(0.60) + (0.70)x(0.30) = 0.18 + 0.21 = 0.39. (b) P(Sunny on Tuesday and Wednesday) = (0.30)x(0.60) = 0.18. Exercise 2.7 P(Long-term success) = P(Long-term success | Regular-season show) x P(Regular- season show) + P(Long-term success | Middle-season show) x P(Middle-season show) = (0.10) x (0.60) + (0.05) x (0.40) = 0.08. Exercise 2.10 Let S1 denote the lamp comes from first shipment, S2 denote the lamp comes from second shipment, and D denote the lamp is defective. We want to compare P(S1 | D) to P(S2 | D). We have P(S1) = 100/150 = 2/3, P(S2) = 50/150 = 1/3, P(D | S1) = 0.04, and P(D | S2) = 0.06. First, P(D) = P(D | S1) x P(S1) + P(D | S2) x P(S2) = 7/150. Therefore, P(S1 | D) = P(D | S1) x P(S1)/P(D) = 8/14, and P(S2 | D) = P(D | S2) x P(S2)/P(D) = 6/14. In conclusion, the lamp is more likely to come from the first shipment. Exercise 2.15

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Dr. Edwin Romeijn ESI 6321 Applied Probability Methods in Engineering Prework Problem Set - Solutions Class of 2009 - 2 - Let X be the number of courses per week. (a) 0.05 + 0.15 + 0.25 + 0.25 + 0.15 + 0.10 + 0.05 = 1. (b) P(X=0) = 0.05. (c) P(X 3) = 0.25 + 0.15 + 0.10 + 0.05 = 0.55. (d) P(X 1) = 1 - P(X = 0) = 1 - 0.05 = 0.95. (e) and (f) Let R denote the net revenue. The following table summarizes the available options. E[R] = \$50,500 and σ (R) = \$22,600. The best option is to add one more instructor (marginal increase of \$800 in net revenues). R
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PreWorkSolution - Dr Edwin Romeijn Prework Problem Set...

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