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Homework 10

Homework 10 - EE 351K PROBABILITY RANDOM PROCESSES...

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EE 351K PROBABILITY & RANDOM PROCESSES FALL 2011 Instructor: Sujay Sanghavi [email protected] Homework 10 Due: December 5th @ ENS 428 Focus: Classical Statistical Inference (Chapter 9 in Textbook) Problem 1 A radar works by transmitting a pulse, and seeing if there is an echo. Ideally, an echo means object is present, and no echo means no object. However, some echoes might get lost, and others may be generated due to other surfaces. To improve accuracy, a radar transmits n pulses, where n is a fixed number, and sees how many echoes it gets. It then makes a decision based on this number. Let p 1 be the probability of an echo for a single pulse when there is no object, and p 2 be the probability when there is an object. Assume p 1 < p 2 . What is the max-likelihood estimation rule for whether the object is present or absent? Problem 2 A source emits a random number of photons K each time that it is triggered. We assume that the PMF of K is p K ( k ; θ ) = c ( θ ) e - θk , k = 0 , 1 , 2 , . . . .

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Homework 10 - EE 351K PROBABILITY RANDOM PROCESSES...

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