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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2008 • Question 8

Question

Math 6010 • Linear Models Fall 2008 • Question 8

Let \(X_1,\ldots ,X_n\) be independent identically distributed random variables with distribution function \(F\). We assume that \(F\) is strictly increasing and continuous on its support. Let \(x_{1/2}\) denote the median.

a. Find a \(1-\alpha \) confidence interval for \(x_{1/2}\). (5 points)

b. Provide a large sample approximation for the confidence interval. (5 points)

Raw LaTeX

Let \(X_1,\ldots,X_n\) be independent identically distributed random
variables with distribution function \(F\). We assume that \(F\) is strictly
increasing and continuous on its support. Let \(x_{1/2}\) denote the median.

a. Find a \(1-\alpha\) confidence interval for \(x_{1/2}\). (5 points)

b. Provide a large sample approximation for the confidence interval. (5 points)

Topic Tags

Covariance and Independence Estimator Distributions Simultaneous Confidence Intervals Uniform Integrability and Truncation Methods