ProblemSet5

# Discrete-Time Signal Processing (2nd Edition) (Prentice-Hall Signal Processing Series)

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Electrical Engineering 431 Problem Set V Due: March 12, 2004 5.1 Laplacian Random Variables A random variable is said to be Laplacian if its probability density function has the form where and are positive constants. (a) Determine the relationship between and so that is a density. (b) Find the probability distribution function . (c) Reparameterize the Laplacian distribution in terms of the variance . (d) Find the probability that the random variable lies between and . (e) What is the probability of given that ? 5.2 Probabilistic Football A football team, which shall remain nameless, likes to mix passing and running plays. The yardage gained on a running play is a random variable uniformly distributed between and yards regardless of the yardage gained on any other play. The team’s quarterback, Bob Linguini, has a strange quirk: the yardage gained on a passing play depends on the previous play. If the previous play was a running play, the yardage gained passing is a random variable uniformly distributed between and yards. If the previous play was a passing play that gained

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