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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2008 • Question 3

Question

Math 6010 • Linear Models Spring 2008 • Question 3

Construct three random variables \(X,Y,Z\) such that \[ \mathbb {E}[\mathbb {E}[X\mid Y]\mid Z]\neq \mathbb {E}[\mathbb {E}[X\mid Z]\mid Y] \] with positive probability.

Raw LaTeX

Construct three random variables \(X,Y,Z\) such that
\[
  \E[\E[X\mid Y]\mid Z]\neq \E[\E[X\mid Z]\mid Y]
\]
with positive probability.

Topic Tags

Classical Probability and Inclusion-Exclusion Convergence in Probability and Almost Sure Convergence Measure-Theoretic Probability Uniform Integrability and Truncation Methods