homewk9

# homewk9 - 4 Hint To make this relatively easy consider the...

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IEOR 4106: Introduction to Operations Research: Stochastic Models Spring 2009, Professor Whitt Homework Assignment 9: Tuesday, April 7. Due on Tuesday, April 14. Chapter 7: Renewal Theory and its Applications In Ross, read Sections 7.1-7.3 up to, but not including, Example 7.8. Skip Remark (ii) in Section 7.2 and Examples 7.1 and 7.3. Also Read Section 7.4 up to, but not including, Example 7.13. (The total required reading is approximately 12 pages.) Do the following exercises at the end of Chapter 7. You need not turn in problems with answers in the back. 1. Hint: See the beginning of Section 7.2. 2. Hint: See Sections 2.2.4 and 7.2. Recall that the sum of independent Poisson random variables has a Poisson distribution. . 3. (answer in back) Hint: See Example 7.2 and following Remark (i).
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Unformatted text preview: 4. Hint: To make this relatively easy, consider the special case of deterministic times between renewals. 7. 8. (answer in back) Hint: Look at Section 7.3. 21. 22. (answer in back) Hint: Look at Section 7.4. 23. 9. Hint: Let T be the time it takes to complete a job. Let W be the time it would take to complete the ﬁrst job attempted. Let S be the time of the ﬁrst shock. To compute E [ T ], develop an equation for it, by conditioning on the possible outcomes of W ; i.e., compute E [ T ] by computing E [ E [ T | W ]]. To compute E [ T | W = w ], compute E [ T | W = w,S = x ], multiply by the density f S ( x ) and integrate over x . (We put Problem 9 last, because it seems a bit harder.) Extra Take-Home-Exam Problem: 7.12....
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