hmk#3_s-2.pdf - ESE503 Simulation Modeling...

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ESE503 - Simulation Modeling & Analysis (Homework #3) Spring Semester, 2018 M. Carchidi –––––––––––––––––––––––––––––––––––– Instructions: 1.) Do the following fi ve (5) Problems and Simulation Problem #2. 2.) Please indicate in the table below whether the problem is submit- ted electronically or in hard copy (or both). 3.) Indicate any optional comments that might assist us in interpret- ing your submission. 4.) For electronic submissions please create a separate fi le for each problem. Also, use the following naming format for all electronic submissions: Example : Your Name HW3 Problem1 . xls . 5.) Submit this cover sheet in order with you assignment. 6.) Homework is due on 03/01/18. No late submissions allowed. –––––––––––––––––––––––––––––––––––– Your Name _____________________ Problem Electronic Paper Number Submission Submission Both Optional Comments 1 2 3 4 5 SP#2 X Must be Done ––––––––––––––––––––––––––––––––––––
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–––––––––––––––––––––––––––––––––––– Problem #1 (15 points) - Arrivals Into A Bank Statistical analysis has revealed that the yearly age distribution of all the people in a small community that use a speci fi c bank is uniform over the range [ a, b ) with a = 42 , b = 78 . a.) (5 points) On a given day, compute the probability that the 7 th customer entering the bank is between 50 and 70 years of age. b.) (5 points) On a given day, compute the probability that the 7 th customer entering the bank is also the 3 rd customer who is between 50 and 70 years of age. c.) (5 points) With 7 people presently in the bank, compute the probability that 3 of them are between 50 and 70 years of age. –––––––––––––––––––––––––––––––––––– Problem #2 (25 points) - The World Series a.) (10 points) In the World series, two teams play until one team has won four games. Suppose that team #1 has a probability of p to win each game (so that team #2 has a probability of 1 p of winning and there can be no ties). Determine (in terms of p ) the probability that the World series will last (a) 4 games, (b) 5 games, (c) 6 games, or (d) 7 games . Then run a Monte-Carlo simulation using 1000 trials to numerically check your results for p = 1 / 4 , 1 / 2 , and 3 / 4 . b.) (15 points) Generalize your results in part (a) by assuming that in the World series, two teams play until one team has won n games for some fi xed value of n , by fi nding the probability (in terms of p , n and x ) that the World series will last exactly x games for x = n, n + 1 , n + 2 , . . . , 2 n 1 . –––––––––––––––––––––––––––––––––––– 2
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–––––––––––––––––––––––––––––––––––– Problem #3 (15 points) - Will You Be Delayed When going to and from work, a driver follows the route shown in the fi gure below. This
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