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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2007 • Question 5

Question

Math 6010 • Linear Models Fall 2007 • Question 5

Let \(X_1\) and \(X_2\) be independent standard normal random variables. Find the necessary and sufficient condition for the independence of \(Y_1=a_1X_1+a_2X_2\) and \(Y_2=b_1X_1+b_2X_2\). (7 points)

Raw LaTeX

Let \(X_1\) and \(X_2\) be independent standard normal random
variables. Find the necessary and sufficient condition for the independence of
\(Y_1=a_1X_1+a_2X_2\) and \(Y_2=b_1X_1+b_2X_2\). (7 points)

Topic Tags

Central Limit Theorems Conditional Expectation and Conditional Independence Covariance and Independence Uniform Integrability and Truncation Methods