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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2016 • Question 1

Question

Math 6010 • Linear Models Fall 2016 • Question 1

Let \(X_1,X_2,\ldots ,X_n\) be iid with common pdf \(f(x)=2x\), \(0<x<1\) and zero elsewhere. Find the limiting distribution of \(n(1-X_{(n)})\), where \(X_{(n)}=\max \{X_1,\ldots ,X_n\}\).

Raw LaTeX

Let \(X_1,X_2,\ldots,X_n\) be iid with common pdf \(f(x)=2x\),
\(0<x<1\) and zero elsewhere. Find the limiting distribution of
\(n(1-X_{(n)})\), where \(X_{(n)}=\max\{X_1,\ldots,X_n\}\).

Topic Tags

Estimator Distributions Multivariate Normal Distributions Uniform Integrability and Truncation Methods Weak Convergence and Distributional Limits