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3044hw2s09 - 3 Suppose X 1 X 12 are i.i.d uniform(5 19 and...

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1 ISyE 3044 – Spring 2009 Homework #2 — Due Monday, 9 February 1. Exercise 5.4 from the text GSWA. Assume that each arriving box contains one widget. In order to get quite accurate point estimators, run the simulation for 7, 24-hour days. Your submission should include a snapshot of the system during execution, a printout of the model logic (*.m file), a timeline graph of the contents of the initial waiting area (try a few plot parameters in order to get a nice plot), and a printout of the final report with the requested values circled or highlighted. 2. Redo Problem 1 assuming that the inspector cannot take a break until s/he is idle. Feel free to model the breaks either with a dummy load or with a resource cycle. In the latter case, print the window displaying the resource cycle. Does the modification have an effect on the performance of the system? Do the queues tend to become smaller? Does it impact
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Unformatted text preview: 3. Suppose X 1 , . . . , X 12 are i.i.d. uniform(5 , 19), and let ¯ X = 12-1 ∑ 12 i =1 X i . Use the central limit theorem to approximate the probability Pr( ¯ X ≤ 13). 4. Suppose X ∼ Poisson(2) and Y ∼ Poisson(1) are independent. ±ind Pr( X + Y ≤ 3). 5. At a nuclear plant, (minor) accidents occur to a Poisson process with a rate of one every two years. (a) What is the probability that the time between successive accidents is greater than two years? (b) What is the probability that 4 or more accidents will occur in a two-year interval? (c) What is the mean number of accidents in ten years? (d) Suppose that a year has passed since the last accident. What is the probability that the next accident will occur at least three years from now? 6. [Will not be graded] Exercises 1, 2, 6, 7, 14, 19, 21, 30, 38, 39, 40, and 52 from Chapter 5 of BCN&N....
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