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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Summer 2020 • Question 4

Question

Math 6010 • Linear Models Summer 2020 • Question 4

Let \(X_1,X_2,\ldots ,X_n\) be independent and identically distributed exponential\((\lambda )\) random variables, meaning that their pdf is \[ f(t)= \begin {cases} 0, & \text {if } -\infty <t<0,\\ \dfrac {1}{\lambda }e^{-t/\lambda }, & \text {if } 0\leq t<\infty . \end {cases} \] Find the uniformly minimum variance unbiased estimator for \(\tau =\lambda ^5\).

Raw LaTeX

Let \(X_1,X_2,\ldots,X_n\) be independent and identically distributed
exponential\((\lambda)\) random variables, meaning that their pdf is
\[
  f(t)=
  \begin{cases}
    0, & \text{if } -\infty<t<0,\\
    \dfrac{1}{\lambda}e^{-t/\lambda}, & \text{if } 0\leq t<\infty.
  \end{cases}
\]
Find the uniformly minimum variance unbiased estimator for \(\tau=\lambda^5\).

Topic Tags

Covariance and Independence Estimator Distributions Sufficiency, Completeness, and UMVUE Uniform Integrability and Truncation Methods