{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online