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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

2005 • Question 4

Question

Math 6010 • Linear Models 2005 • Question 4

Let \(X_1,\ldots ,X_n\) be independent, identically distributed random variables with a continuous distribution function \(F\). Let \(x_{1/4}\) be defined by \(F(x_{1/4})=1/4\).

(a) Find a \(1-\alpha \) lower confidence bound for \(x_{1/4}\).

(b) Provide a large sample approximation.

Raw LaTeX

Let \(X_1,\ldots,X_n\) be independent, identically distributed random variables with a continuous distribution function \(F\). Let \(x_{1/4}\) be defined by \(F(x_{1/4})=1/4\).

(a) Find a \(1-\alpha\) lower confidence bound for \(x_{1/4}\).

(b) Provide a large sample approximation.

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Topic Tags

Covariance and Independence Estimator Distributions Multivariate Normal Distributions Uniform Integrability and Truncation Methods