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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

2004 • Question 3

Question

Math 6010 • Linear Models 2004 • Question 3

Let \(X_1\) and \(X_2\) be two independent, identically distributed exponential (1) random variables. Compute the joint density of \(Y_1=X_1+X_2\) and \(Y_2=X_1/(X_1+X_2)\).

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Let \(X_1\) and \(X_2\) be two independent, identically distributed exponential (1) random variables. Compute the joint density of \(Y_1=X_1+X_2\) and \(Y_2=X_1/(X_1+X_2)\).

Topic Tags

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