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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

2004 • Question 6

Question

Math 6010 • Linear Models 2004 • Question 6

Let \(X_1,X_2,\ldots ,X_n\) be independent, identically distributed Poisson \((\theta )\) random variables. Find the uniformly minimum unbiased estimator for \(\eta =\theta ^2 e^{-\theta }\). (You must explain your answer.)

Raw LaTeX

Let \(X_1,X_2,\ldots,X_n\) be independent, identically distributed Poisson \((\theta)\) random variables. Find the uniformly minimum unbiased estimator for \(\eta=\theta^2 e^{-\theta}\). (You must explain your answer.)

Topic Tags

Covariance and Independence Estimator Distributions Measure-Theoretic Probability Uniform Integrability and Truncation Methods