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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2015 • Question 1

Question

Math 6010 • Linear Models Spring 2015 • Question 1

Let \(X_1,X_2,\ldots ,X_n\) be a random sample from the Poisson distribution with parameter \(\lambda >0\). Use the Rao–Blackwell theorem and/or the Lehmann–Scheffé theorem to find a UMVUE of \(\mathbb {P}\{X_1=0\}=e^{-\lambda }\).

Raw LaTeX

Let \(X_1,X_2,\ldots,X_n\) be a random sample from the Poisson
distribution with parameter \(\lambda>0\). Use the Rao--Blackwell theorem and/or
the Lehmann--Scheff\'e theorem to find a UMVUE of
\(\Prob\{X_1=0\}=e^{-\lambda}\).

Topic Tags

Estimator Distributions Multivariate Normal Distributions Sufficiency, Completeness, and UMVUE Uniform Integrability and Truncation Methods