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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2009 • Question 1

Question

Math 6010 • Linear Models Spring 2009 • Question 1

Let \(X_1\) and \(X_2\) be independent, each with probability density function \(f(x)=1/x^2\), \(x>1\). Find the joint probability density function of \(Y_1=X_1X_2\) and \(Y_2=X_1/X_2\). It is important to state where your formula is valid. (If you have time, check that your joint pdf integrates to 1; if it doesn’t, find the error.)

Raw LaTeX

Let \(X_1\) and \(X_2\) be independent, each with probability density
function \(f(x)=1/x^2\), \(x>1\). Find the joint probability density function of
\(Y_1=X_1X_2\) and \(Y_2=X_1/X_2\). It is important to state where your formula is
valid. (If you have time, check that your joint pdf integrates to 1; if it
doesn't, find the error.)

Topic Tags

Classical Probability and Inclusion-Exclusion Covariance and Independence Measure-Theoretic Probability Uniform Integrability and Truncation Methods