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PS 1 10

# PS 1 10 - University of Minnesota Dept of Electrical and...

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University of Minnesota Dept. of Electrical and Computer Engineering EE 8581 DETECTION AND ESTIMATION THEORY Spring 2010 Problem Set 1 Assigned: February 2, 2010 Due: February 9, 2010 Readings : Read Levy Sections 2.1- 2.6. Problems : Solve problems 2.2, 2.4 and 2.5 in Chapter 2 of Levy’s book and the following problems: Problem 1: Suppose that a sequence of observations r 1 , r 2 , r 3 ,... has the following two hypothesized probabilistic descriptions: H0: r 1 = x + n 1 H1: r 1 = x + n 1 r 2 = x + n 2 r 2 = 2x + n 2 r 3 = x + n 3 r 3 = 4x + n 3 . . . . . . r k = x + n k r k = 2 (k-1) x + n k where x and the n i are all independent Gaussian random variables. The variable x has mean 0 and variance 1, while each n i has mean 0 and variance σ 2 . a) Determine the likelihood ratio L(r 1, r 2, r 3 )= p(r 1, r 2, r 3 |H 1 ) p(r 1, r 2, r 3 |H 0 ) b) Find a sufficient statistic for the optimum test that is a quadratic function of the r i . c)

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PS 1 10 - University of Minnesota Dept of Electrical and...

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