A3 Independent Observations X1 X2 X Are Sampled From A Poisson Distribution With Parameter X 0 A Varjable U 1 (49.71 KiB) Viewed 97 times
A3 Independent Observations X1 X2 X Are Sampled From A Poisson Distribution With Parameter X 0 A Varjable U 2 (4.84 KiB) Viewed 97 times
A3 Independent observations, X1, X2...., X., are sampled from a Poisson distribution with parameter x > 0. A varjable U is defined such that U = 1 if Xi = 0 and U = 0 if Xi > 0. We wish to estimate ode- 1. Show that U is an unbiased estimator of . [2] 2. Write down the likelihood of given the observations, {Xi = 1; i = 1,...,n), and explain why S = D., X, is sufficient for o. [3] TURN OVER Examination Paper for STAT3001, 2017 Page 4 3. Derive the corresponding Score function, and explain carefully whether or not an un- biased estimator of o exists with a variance achieving the Cramer-Rao lower bound. 4. State the marginal distributions of S and of W = XL,X, [3] 5. Use your answers given above to find the conditional expectation, T =E(US) of U given S and explain, without proof but quoting any relevant theorems, why T is the Minimum Variance Unbiased Estimator of . [6]
answer 3 and 5
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