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5500HW3 - ORIE 3500/5500 Fall Term 2008 Assignment 3 Note...

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ORIE 3500/5500 Fall Term 2008 Assignment 3 Note that the due date is Monday, September 29 , at 1:00 pm you need to mention your section number on the top of your answer script. 1. [4 + 3 = 7 pts] Suppose that X is a discrete random variable with PMF p X ( r ) = a + b · r, r = 1 , 2 , . . . , 5 , for some constants a and b . If E ( X ) = 11 / 3, (a) find the numerical values of a and b , and (b) find var ( X ). 2. [3 + 3 + 2 = 8 pts] Suppose that according to the government estimate 75% college-students of NY state own a car. To verify that 20 investigators are appointed. They were sent to 20 different colleges and each is asked to interview 5 randomly chosen students. If the government estimate is correct, (a) what is the probability that the first investigator finds at least one student who does not own a car? (b) Let N be the number of investigators who find at least one student who does not own a car. Find the PMF of N . (c) Find E ( N ). 3. [3 + 2 + 3 + 5 = 13 pts] Let N be the number of telephone calls received in a telephone exchange between 9 and 10 a.m. The calls are forwarded with equal probability to one of the 4 offices. Let X be the number of calls received in the
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