problem set5 - ELEC 531 STATISTICAL SIGNAL PROCESSING...

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ELEC 531: STATISTICAL SIGNAL PROCESSING Department of Electrical and Computer Engineering Rice University Fall 2007 Problem Set 5 Due: October 9, 2007 Problem 5.1 Imagine yourself idly standing on the corner in a large city when you note the serial number of a passing beer truck. Because you are idle, you wish to estimate (guess may be more accurate here) how many beer trucks the city has from this single observation. (a) Making appropriate assumptions, the beer truck’s number is drawn from a uni- form probability density ranging between zero and some unknown upper limit, find the maximum likelihood estimate of the upper limit. (b) Show that this estimate is biased. (c) In one of your extraordinarily idle moments, you observe throughout the city L beer trucks. Assuming them to be independent observations, now what is the maximum likelihood estimate of the total? (d) Is this estimate of θ biased? asymptotically biased? efficient?
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