# hw8 - by more that 15 minutes. ( b ) Estimate the...

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ORIE 3500/5500 – Engineering Probability and Statistics II Fall 2010 Assignment 8 Problem 1 The weekly demand for a product has, approximately, a normal distribution with mean 1 , 000 and standard deviation 200. The current on hand inventory is 2 , 200, and no deliveries will be occurring in the next two weeks. Assuming that the demands in diﬀerent weeks are independent, ( a ) what is the probability that the demands in each of the next two weeks is less than 1 , 100? ( b ) what is the probability that the total of the demands in the next two weeks exceeds 2 , 200? Problem 2 The number of minutes that airline ﬂights are behind the schedule follow a gamma distribution with the shape parameter α = 3 and scale parameter λ = 1 / 4. ( a ) Find the probability that a randomly selected ﬂight will be late
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Unformatted text preview: by more that 15 minutes. ( b ) Estimate the probability in part ( a ) using Markovs inequality. How does the bound compare with the exact answer? Problem 3 If X and Y are independent -square random variables with 1 and 2 degrees of freedom respectively, determine the probability that X + Y exceeds 5. Problem 4 For a Poisson random variable X with mean = 6, calculate P ( X 4 exactly, and using a normal approximation. Are the results similar? Problem 5 Let be the standard normal distribution function. If, for some constants a and b > 0, P ( X x ) = x-a b , characterize the distribution of X . Due: November 1, at 4 p.m. 1...
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## This note was uploaded on 11/11/2010 for the course ORIE 3500 at Cornell University (Engineering School).

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