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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2010 • Question 8

Question

Math 6010 • Linear Models Spring 2010 • Question 8

Let \(X_1,\ldots ,X_n\) denote an independent sample from an exponential distribution with [unknown] mean \(\theta >0\). What does the Neyman–Pearson lemma say about \(H_0:\theta =1\) versus \(H_a:\theta =2\)? Explain carefully, and identify explicitly the rejection region.

Raw LaTeX

Let \(X_1,\ldots,X_n\) denote an independent sample from an exponential
distribution with [unknown] mean \(\theta>0\). What does the Neyman--Pearson lemma
say about \(H_0:\theta=1\) versus \(H_a:\theta=2\)? Explain carefully, and identify
explicitly the rejection region.

Topic Tags

Covariance and Independence Estimator Distributions Multivariate Normal Distributions Uniform Integrability and Truncation Methods