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Unformatted text preview: Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.432 Stochastic Processes, Detection and Estimation Problem Set 6 Spring 2004 Issued: Tuesday, March 16, 2004 Due: Thursday, April 1, 2004 Reading: This problem set: Sections 4.0-4.5 and Section 4.7 except 4.7.5 Next: Sections 4.3-4.6, 4.A, 4.B, Chapter 5 Final Exam is on May 19, 2004, from 9:00am to 12:00 noon You are allowed to bring three 8 1 × 11 sheets of notes (both 2 sides). If you have a conﬂict with this time and need to schedule an alternate time, you must see Prof. Willsky by April 6, 2004 at the absolute latest. Problem 6.1 Consider the estimation of a nonrandom but unknown parameter x from an observa- tion of the form y = x + w where w is a random variable. Two different scenarios are considered in parts (a) and (b) below. (a) Suppose w is a zero-mean Laplacian random variable. i.e., p w ( w ) = e − | w | 2 for some > 0. Does an unbiased estimate of x exist? Explain. Does an eﬃcent estimate of x exist? If so, determine ˆ x eff ( y ). If not, explain. 2 2 Hint: w e − | w | dw = ....
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- Spring '04
- Electrical Engineering, Probability theory, Stochastic process, Gaussian Random Process, typical sample function