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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

2006 • Question 9

Question

Math 6010 • Linear Models 2006 • Question 9

Let \(X\) and \(Y\) be two standard-normal random variables.

(a) Prove that if \((X,Y)\) is Gaussian then \(X\) and \(Y\) are independent.

(b) Construct an example wherein \((X,Y)\) is not a (two-dimensional) Gaussian random variable.

Raw LaTeX

Let \(X\) and \(Y\) be two standard-normal random variables.

\textbf{(a)} Prove that if \((X,Y)\) is Gaussian then \(X\) and \(Y\) are independent.

\textbf{(b)} Construct an example wherein \((X,Y)\) is not a (two-dimensional)
Gaussian random variable.

Topic Tags

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