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Unformatted text preview: ECE 154B Winter 2007 Homework #2 Due: Monday, January 29 1. Consider the 2 hypotheses problem where the a priori probabilities for the two hypotheses are: π = ¾ and π 1 = ¼. Let the conditional probability densities of the observable Y under the two hypotheses be: f Y|0 (y) = K 1 y for 0 < y < 3, f Y|0 (y) = 0 elsewhere and f Y|1 (y) = K 2 for 0 < y < 3, f Y|1 (y) = 0 elsewhere. (You must first determine the constants K 1 and K 2. ). a. Find the decision rule that minimizes the probability of error. b. Calculate the probability of error for this decision rule. c. Verify your calculation of the probability of error by simulation. 2. Consider the 4 hypotheses problem with 4 equally likely hypotheses (H , H 1 , H 2 , H 3 ) . Under each of the 4 hypotheses assume that the observable Y is a Gaussian random variable with means (-3, -1, +1, +3) respectively. Under each hypotheses assume that the Gaussian has variance 5....
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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.
- Winter '07