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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2019 • Question 2

Question

Math 6010 • Linear Models Spring 2019 • Question 2

Let \(X_n:\Omega \to \mathbb {R}\) be a sequence of integrable random variables with the same distribution. Prove that \(X_n/n\to 0\) almost surely. Hint: Borel-Cantelli.

Raw LaTeX

Let \(X_n:\Omega\to\mathbb{R}\) be a sequence of integrable random
variables with the same distribution. Prove that \(X_n/n\to0\) almost surely.
\textbf{Hint:} Borel-Cantelli.

Topic Tags

Borel-Cantelli Lemmas Convergence in Probability and Almost Sure Convergence Estimator Distributions Uniform Integrability and Truncation Methods