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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

1993 • Question 4

Question

Math 6010 • Linear Models 1993 • Question 4

Suppose that \(X\) and \(Y\) are independent. Let \(f\) be a Borel function on \(\mathbb {R}^2\) with \(E[|f(X,Y)|]<\infty \) and let \(g(x)=E[f(x,Y)]\). Show that \(E[f(X,Y)\mid X]=g(X)\).

Raw LaTeX

Suppose that \(X\) and \(Y\) are independent. Let \(f\) be a Borel function on \(\mathbb{R}^2\) with \(E[|f(X,Y)|]<\infty\) and let \(g(x)=E[f(x,Y)]\). Show that \(E[f(X,Y)\mid X]=g(X)\).

Topic Tags

Covariance and Independence Uniform Integrability and Truncation Methods