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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2009 • Question 6

Question

Math 6010 • Linear Models Spring 2009 • Question 6

Assume a sample of size \(n\) from \(\operatorname {Uniform}[\eta -\theta ,\eta +\theta ]\), which is a location-scale family. Here \(\eta \) is real and \(\theta >0\).

(a) Find a \(100(1-\alpha )\%\) confidence interval for \(\theta \).

(b) Find a \(100(1-\alpha )\%\) confidence interval for \(\eta \).

It is not necessary to find the explicit distribution of the pivotal quantities; just denote the needed quantiles by \(x_p\) and \(y_p\) for an appropriate \(p\).

Raw LaTeX

Assume a sample of size \(n\) from \(\UNIF[\eta-\theta,\eta+\theta]\),
which is a location-scale family. Here \(\eta\) is real and \(\theta>0\).

\textbf{(a)} Find a \(100(1-\alpha)\%\) confidence interval for \(\theta\).

\textbf{(b)} Find a \(100(1-\alpha)\%\) confidence interval for \(\eta\).

It is not necessary to find the explicit distribution of the pivotal quantities;
just denote the needed quantiles by \(x_p\) and \(y_p\) for an appropriate \(p\).

Topic Tags

Estimator Distributions Multivariate Normal Distributions Simultaneous Confidence Intervals Uniform Integrability and Truncation Methods