Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2008 • Question 7

Question

Math 6010 • Linear Models Fall 2008 • Question 7

Let \(X_1,\ldots ,X_n\) be independent identically distributed Poisson random variables with parameter \(\theta _1\). Let \(Y_1,\ldots ,Y_m\) be independent identically distributed Poisson random variables with parameter \(\theta _2\). We assume that the two samples are independent. We wish to test \(H_0:\theta _1=\theta _2\) against the alternative that \(H_0\) is not true.

a. Derive the likelihood ratio test. (5 points)

b. Provide a large sample approximation for the rejection region. (2 points)

Raw LaTeX

Let \(X_1,\ldots,X_n\) be independent identically distributed Poisson
random variables with parameter \(\theta_1\). Let \(Y_1,\ldots,Y_m\) be
independent identically distributed Poisson random variables with parameter
\(\theta_2\). We assume that the two samples are independent. We wish to test
\(H_0:\theta_1=\theta_2\) against the alternative that \(H_0\) is not true.

a. Derive the likelihood ratio test. (5 points)

b. Provide a large sample approximation for the rejection region. (2 points)

Topic Tags

Covariance and Independence F-Tests and t-Tests Likelihood Ratio Tests Maximum Likelihood Estimation