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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2018 • Question 1

Question

Math 6010 • Linear Models Fall 2018 • Question 1

Let \(X_1,X_2\) be iid with density \[ f(x;\theta )= \begin {cases} 3x^2/\theta ^3, & 0<x<\theta ,\\ 0, & \text {otherwise.} \end {cases} \] Find a complete, sufficient statistic for \(\theta \in [0,\infty )\) based on \(X_1\) and \(X_2\).

Raw LaTeX

Let \(X_1,X_2\) be iid with density
\[
  f(x;\theta)=
  \begin{cases}
    3x^2/\theta^3, & 0<x<\theta,\\
    0, & \text{otherwise.}
  \end{cases}
\]
Find a complete, sufficient statistic for \(\theta\in[0,\infty)\) based on \(X_1\)
and \(X_2\).

Topic Tags

Estimator Distributions Measure-Theoretic Probability Sufficiency, Completeness, and UMVUE Uniform Integrability and Truncation Methods