Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

2004 • Question 4

Question

Math 6010 • Linear Models 2004 • Question 4

Let \(X_1,X_2,\ldots ,X_n\) be independent, identically distributed uniform on \([0,\theta ]\), \(\theta >0\), random variables. We wish to test \(H_0:\theta \leq \theta _0\) against \(H_A:\theta >\theta _0\). Find the uniformly most powerful test of size \(\alpha \) and compute the power function. (You must explain why your test has this property.)

Raw LaTeX

Let \(X_1,X_2,\ldots,X_n\) be independent, identically distributed uniform on \([0,\theta]\), \(\theta>0\), random variables. We wish to test \(H_0:\theta\leq\theta_0\) against \(H_A:\theta>\theta_0\). Find the uniformly most powerful test of size \(\alpha\) and compute the power function. (You must explain why your test has this property.)

Topic Tags

Covariance and Independence F-Tests and t-Tests Measure-Theoretic Probability Uniform Integrability and Truncation Methods