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

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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 λe - λ | x | , for x R , then X is said to have the double exponential distribution with parameter λ . Find the mean and variance of such a random variable. Hint: you could use moment generating functions, although it’s not required. Problem 3. Find the moment generating function of the binomial( n, p ) random variable, where n 1 and 0 < 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 be discovered on the 15th trial?
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