Homework_1_2007

Homework_1_2007 - ECE 154B Winter 2007 Homework#1 Due...

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ECE 154B Winter 2007 Homework #1 Due: Monday, January 22 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 ). 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. Find the decision regions that minimize the probability of error in choosing amongst the two hypotheses H 0 and H 1 , based upon the scalar observation r. Assume that the apriori probabilities for the two hypotheses are:

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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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Homework_1_2007 - ECE 154B Winter 2007 Homework#1 Due...

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