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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Summer 2020 • Question 6

Question

Math 6010 • Linear Models Summer 2020 • Question 6

Let \(X_1,\ldots ,X_n\) be independent and identically distributed random variables with density function \[ h(t;\theta )=\frac {3t^2}{\theta ^3}1\{0\leq t\leq \theta \}, \] where \(\theta >0\) is a parameter. Find a \(100(1-\alpha )\%\), two-sided, equal-tailed confidence interval for \(\theta \).

Raw LaTeX

Let \(X_1,\ldots,X_n\) be independent and identically distributed
random variables with density function
\[
  h(t;\theta)=\frac{3t^2}{\theta^3}1\{0\leq t\leq\theta\},
\]
where \(\theta>0\) is a parameter. Find a \(100(1-\alpha)\%\), two-sided,
equal-tailed confidence interval for \(\theta\).

Topic Tags

Covariance and Independence Measure-Theoretic Probability Simultaneous Confidence Intervals Uniform Integrability and Truncation Methods