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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 \(\theta>0\).

(a) Find the maximum likelihood estimator \(\hat{\theta}\) for \(\theta\);

(b) Construct a \(100(1-\alpha)\%\) confidence interval for \(\theta\) based on
\(\hat{\theta}\).

Topic Tags

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