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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

2000 • Question 1

Question

Math 6010 • Linear Models 2000 • Question 1

Let \(X_1,X_2,X_3,\ldots \) be independent and exponential with mean 1. Use the Borel–Cantelli lemmas to show that \(\limsup _{n\to \infty }X_n/\log n=1\) a.s.

Raw LaTeX

Let \(X_1,X_2,X_3,\ldots\) be independent and exponential with mean 1.
Use the Borel--Cantelli lemmas to show that
\(\limsup_{n\to\infty}X_n/\log n=1\) a.s.

Topic Tags

Borel-Cantelli Lemmas Convergence in Probability and Almost Sure Convergence Covariance and Independence Uniform Integrability and Truncation Methods