hw06 - ORIE 360/560 Fall 2007 Assignment 6 Due Tuesday,...

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Unformatted text preview: ORIE 360/560 Fall 2007 Assignment 6 Due Tuesday, Oct. 16 at 2:00 pm Please remember to show your work! Please remember to put your section number and net id on the assignment! Problem 1. Suppose X has an exponential distribution, and that P [ X > . 01] = 1 / 2. Find the unique number t satisfying P [ X > t ] = . 9. Problem 2. If X has density f X ( x ) = 1 2 e- | x | , for x R , then X is said to have the double exponential distribution with parameter . Find the mean and variance of such a random variable. Hint: you could use moment generating functions, although its not required. Problem 3. Find the moment generating function of the binomial( n,p ) random variable, where n 1 and < p < 1. Use the result to check the values for the mean and variance given in class (or in the text). Problem 4. A contractor purchases a shipment of 100 widgets, 20 of which are defective. (a) If the contractor tests the widgets one by one, what is the probability that the first defective widget will...
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