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Homework 9

# Homework 9 - EE 351K PROBABILITY RANDOM PROCESSES...

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FALL 2011 Instructor: Sujay Sanghavi Homework 9 Due: November 22th in class Focus: ML Estimation (Chapter 9.1 in Textbook) Problem 1 The parameter of an exponential random variable has to be estimated from one sample. What is the ML estimator? Is it unbiased? Problem 2 Alice models the time that she spends each week on homework as an exponentially distributed random variable with unknown parameter θ . Homework times in different weeks are independent. After spending 10, 14, 18, 8, and 20 hours in the ﬁrst 5 weeks of the semester, what is her ML estimator of θ ? Problem 3 X is known to be a uniform random variable, with range [ - a, a ] . However, the parameter a 0 is unknown, and has to be estimated from n samples. (a) What is the ML estimator? (b) Is it unbiased? (c) Is it consistent? Problem 4 A photodetector has a probability p of capturing each photon incident on it. A light source is exposed to the detector, and a million photons are captured. What is the ML estimate of the number of photons actually

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Homework 9 - EE 351K PROBABILITY RANDOM PROCESSES...

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