Solution_1_2007

Solution_1_2007 - ECE 154B Winter 2007 Homework #1...

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ECE 154B Winter 2007 Homework #1 Solutions 1. In order to do some simulations, one must be able to generate samples of random variables with arbitrary probability distributions. Most programming languages have a command that generates samples for a random variable X that is uniformly distributed over the interval (0,1) but we can obtain samples for an arbitrary distribution by using a nonlinear transformation y = g(x). a. Find g(x) if the probability distribution for Y is given as: p(y) = K 1 y for 0 < y < 3 and p(y) = 0 elsewhere. (You must first determine the constant K 1 ). 0 3 K 1 ydy = 1 K 1 y 2 2 0 3 = 1 K 1 = 2 9 f y = { 2 9 y , 0 y 3 0 , else } = { dg 1 y dy , 0 g 1 y ≤ 1 0 , else } dg 1 y dy = 2 9 y g 1 y = y 2 9 C g 1 3 = 1 C = 1 C = 0 x = g x 2 9 g x = 3 x b. Find g(x) if the probability distribution for Y is given as: p(y) = K 2 for -2 < y < 3 and p(y) = 0 elsewhere. (You must first determine the constant K 2 ). 2
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This note was uploaded on 11/11/2009 for the course ECE 670377 taught by Professor Wolf during the Winter '07 term at UCSD.

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Solution_1_2007 - ECE 154B Winter 2007 Homework #1...

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