Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2008 • Question 10

Question

Math 6010 • Linear Models Fall 2008 • Question 10

Suppose \(X\) and \(Y\) are independent bounded random variables. Prove in complete detail the following assertions:

(a) \(\mathbb {E}(XY)=\mathbb {E}(X)\mathbb {E}(Y)\),

(b) \(\mathbb {E}(X\mid Y)=\mathbb {E}(X)\).

Raw LaTeX

Suppose \(X\) and \(Y\) are independent bounded random variables.
Prove in complete detail the following assertions:

(a) \(\E(XY)=\E(X)\E(Y)\),

(b) \(\E(X\mid Y)=\E(X)\).

Topic Tags

Covariance and Independence Measure-Theoretic Probability Uniform Integrability and Truncation Methods