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# assign4 - SYSC4005/5001 Simulation of Discrete Event...

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SYSC4005/5001 Simulation of Discrete Event Systems Homework Assignment 4 DUE: March 22 2010 1. For the problem of estimating the parameter θ of a uniform distribution in [0 , θ ] we have already seen in class that one unbiased estimator is W 1 = n + 1 n Y max By following a similar approach as we did in class derive an unbiased estimator of θ based on the minimum observation Y min as W 2 = kY min . Find the parameter k and derive the relative efficiency of W 2 with respect to W 1 2. If a series of independent Bernoulli trials is terminated with the oc- curence of the first success, the probability function for K , the length of the series, will be given by the geometric distribution f K ( k ; p ) = P ( K = k ) = (1 - p ) k - 1 p, k = 1 , 2 , . . . where p is the (unknown)probability of success at any trial. If n such series are observed, the data will consist of n lengths, k 1 , k 2 , . . . , k n . Find a max. likelihood estimator for the parameter p. Justify in detail all your arguments!.

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assign4 - SYSC4005/5001 Simulation of Discrete Event...

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