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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2019 • Question 1

Question

Math 6010 • Linear Models Spring 2019 • Question 1

Let \(X_n\) be a sequence of i.i.d. random variables. Assume that \(\mathbb {P}(X_n\to \infty )>0\). Prove that \(\mathbb {P}(X_0=\infty )=1\). Hint: first prove that \(\mathbb {P}(X_n\to \infty )=1\).

Raw LaTeX

Let \(X_n\) be a sequence of i.i.d. random variables. Assume that
\(\Prob(X_n\to\infty)>0\). Prove that \(\Prob(X_0=\infty)=1\).
\textbf{Hint:} first prove that \(\Prob(X_n\to\infty)=1\).

Topic Tags

Laws of Large Numbers Measure-Theoretic Probability Uniform Integrability and Truncation Methods