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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2017 • Question 6

Question

Math 6010 • Linear Models Spring 2017 • Question 6

If \(X_1,X_2,\ldots \) are independent standard normal random variables, then find non-random sequences \(a_n,b_n\to \infty \) such that \(a_n\min _{1\leq i\leq n}X_i+b_n\) converges weakly. Identify the limiting distribution.

Raw LaTeX

If \(X_1,X_2,\ldots\) are independent standard normal random
variables, then find non-random sequences \(a_n,b_n\to\infty\) such that
\(a_n\min_{1\leq i\leq n}X_i+b_n\) converges weakly. Identify the limiting
distribution.

Topic Tags

Central Limit Theorems Covariance and Independence Multivariate Normal Distributions Weak Convergence and Distributional Limits