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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2017 • Question 10

Question

Math 6010 • Linear Models Spring 2017 • Question 10

Let \(X\) and \(Y\) be two real-valued random variables. Let \(f\) and \(g\) be two non-decreasing measurable functions such that \(f(X)\) and \(g(Y)\) are integrable. Prove that \[ \mathbb {E}[f(X)g(Y)]\geq \mathbb {E}[f(X)]\mathbb {E}[g(Y)]. \]

Raw LaTeX

Let \(X\) and \(Y\) be two real-valued random variables. Let \(f\) and
\(g\) be two non-decreasing measurable functions such that \(f(X)\) and \(g(Y)\) are
integrable. Prove that
\[
  \E[f(X)g(Y)]\geq \E[f(X)]\E[g(Y)].
\]

Topic Tags

Measure-Theoretic Probability Uniform Integrability and Truncation Methods