3044hw2s09 - 3. Suppose X 1 , . . . , X 12 are i.i.d....

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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 Fle), 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 Fnal 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. ±eel 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 modiFcation have an e²ect on the performance of the system? Do the queues tend to become smaller? Does it impact the utilization of the inspector?
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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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This note was uploaded on 11/26/2009 for the course ISYE 3044 taught by Professor Alexopoulos during the Spring '08 term at Georgia Institute of Technology.

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