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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

1999 • Question 6

Question

Math 6010 • Linear Models 1999 • Question 6

Let \(X_1,X_2,\ldots ,X_n\) be independent identically distributed random variables uniform on \([\theta ,\theta +1]\).

  1. Find a sufficient statistic for \(\theta \). (5 points)
  2. Is your statistic complete? (5 points)
  3. Find the maximum likelihood estimator for \(\theta \). (10 points)

Raw LaTeX

Let \(X_1,X_2,\ldots,X_n\) be independent identically distributed random variables uniform on \([\theta,\theta+1]\).
\begin{enumerate}
\item Find a sufficient statistic for \(\theta\). (5 points)
\item Is your statistic complete? (5 points)
\item Find the maximum likelihood estimator for \(\theta\). (10 points)
\end{enumerate}

Topic Tags

Covariance and Independence Estimator Distributions Maximum Likelihood Estimation Sufficiency, Completeness, and UMVUE