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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2016 • Question 2

Question

Math 6010 • Linear Models Fall 2016 • Question 2

Let \(X_1\sim N(0,4\theta )\), \(X_2\sim N(0,9\theta )\), \(X_3\sim N(0,4\theta ^2)\), \(X_4\sim N(0,12\theta ^2)\), and assume that all \(X\)s are independent of each other. Using all four \(X\) variables and the \(t\) distribution, compute a \(100(1-\alpha )\%\) confidence interval for \(\theta \).

Raw LaTeX

Let \(X_1\sim \N(0,4\theta)\), \(X_2\sim \N(0,9\theta)\),
\(X_3\sim \N(0,4\theta^2)\), \(X_4\sim \N(0,12\theta^2)\), and assume that all
\(X\)s are independent of each other. Using all four \(X\) variables and the \(t\)
distribution, compute a \(100(1-\alpha)\%\) confidence interval for \(\theta\).

Topic Tags

Covariance and Independence Estimator Distributions Simultaneous Confidence Intervals Uniform Integrability and Truncation Methods