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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2015 • Question 9

Question

Math 6010 • Linear Models Spring 2015 • Question 9

Let \(X_1\) and \(X_2\) be independent \(\operatorname {Exponential}(1)\) random variables (density \(e^{-x}\), \(x>0\)). Find the joint density of \(Y_1=X_1/X_2\) and \(Y_2=X_1+X_2\). Find the marginal densities of \(Y_1\) and \(Y_2\) as well.

Raw LaTeX

Let \(X_1\) and \(X_2\) be independent \(\EXP(1)\) random variables
(density \(e^{-x}\), \(x>0\)). Find the joint density of \(Y_1=X_1/X_2\) and
\(Y_2=X_1+X_2\). Find the marginal densities of \(Y_1\) and \(Y_2\) as well.

Topic Tags

Covariance and Independence Measure-Theoretic Probability Multivariate Normal Distributions Uniform Integrability and Truncation Methods