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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

1996 • Question 10

Question

Math 6010 • Linear Models 1996 • Question 10
Let \(X_1,\ldots,X_n\) be an i.i.d. sample from a uniform \((0,\theta)\) distribution, where \(\theta>0\). **(a)** Find the maximum likelihood estimator \(\hat{\theta}\) for \(\theta\); **(b)** Construct a \(100(1-\alpha)\%\) confidence interval for \(\theta\) based on \(\hat{\theta}\).

Raw LaTeX

Let \(X_1,\ldots,X_n\) be an i.i.d. sample from a uniform \((0,\theta)\) distribution, where \(\theta>0\).
\begin{parts}
\item Find the maximum likelihood estimator \(\hat{\theta}\) for \(\theta\);
\item Construct a \(100(1-\alpha)\%\) confidence interval for \(\theta\) based on \(\hat{\theta}\).
\end{parts}

Topic Tags

Estimator Distributions Maximum Likelihood Estimation Simultaneous Confidence Intervals Uniform Integrability and Truncation Methods