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homewk2 - 000 000 times What is the approxi-mate...

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IEOR 4106: Introduction to Operations Research: Stochastic Models Homework Assignment 2: Tuesday, January 25, 2011 Due on Tuesday, February at (before) class; to be discussed at the recita- tion on Monday, January 31. More Probability Review: In the Ross textbook, Introduction to Probability Models , read Sections 3.1-3.5 up to (not including) Example 3.24 on p. 125 in the 10th edition (up to Example 3.22 on p. 123 of the 9th edition). To keep the reading under control, Examples 3.14-3.16 on pages 111-117 (Examples 3.13-3.15 on pages 110-116 of the 9th edition) can be omitted. (The rest of Chapter 3 has interesting material, but we will not cover it.) Problems from Chapter 3 of Ross, plus two extra ones. In all homework, show your work. Problem 3.3 Problem 3.4 Problem 3.7 Problem 3.11 Problem 3.12 Problem 3.14 Problem 3.15 Problem 3.37 Problem 3.40 (a) Extra Problem 1. Suppose that you flip a fair coin 1
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Unformatted text preview: , 000 , 000 times. What is the approxi-mate probability of getting more than 501 , 500 heads? Extra Problem 2. Suppose that you own shares of stock in the company Lewser, Inc. Suppose that the current (initial) stock price is $100 per share. Suppose that we regard the daily changes in stock price as independent and identically distributed random variables (a simple additive random walk model). Suppose that the expected daily change is-$0 . 10 or-10 cents per day (as one would expect from a stock with that name). Using units of dollars, suppose that the variance of the daily change is 0 . 25. Suppose that the distribution of the daily change is a gamma distribution. What is the approximate probability that the stock price has not dropped (is at least $100) after 100 days?...
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