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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2009 • Question 2

Question

Math 6010 • Linear Models Spring 2009 • Question 2

Let \(X_1,\ldots ,X_n\) be independent \(\operatorname {LogNormal}(\mu ,\sigma ^2)\) (i.e., \(X_1=e^{Y_1},\ldots ,X_n=e^{Y_n}\) with \(Y_1,\ldots ,Y_n\) being independent \(N(\mu ,\sigma ^2)\)). Argue that the sample median is asymptotically normal and find the asymptotic mean and variance.

Raw LaTeX

Let \(X_1,\ldots,X_n\) be independent \(\LOGN(\mu,\sigma^2)\) (i.e.,
\(X_1=e^{Y_1},\ldots,X_n=e^{Y_n}\) with \(Y_1,\ldots,Y_n\) being independent
\(\N(\mu,\sigma^2)\)). Argue that the sample median is asymptotically normal and
find the asymptotic mean and variance.

Topic Tags

Analysis of Variance Covariance and Independence Uniform Integrability and Truncation Methods