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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2016 • Question 3

Question

Math 6010 • Linear Models Spring 2016 • Question 3

Let \(X_1\) and \(X_2\) be independent with joint pdf \(f(x)=x^{-2}\) for \(1\leq x<\infty \) and 0 otherwise.

(a) Find the joint pdf of \(U=X_1X_2\) and \(V=X_2\).

(b) Find the marginal pdf of \(U\).

Raw LaTeX

Let \(X_1\) and \(X_2\) be independent with joint pdf \(f(x)=x^{-2}\) for
\(1\leq x<\infty\) and 0 otherwise.

\textbf{(a)} Find the joint pdf of \(U=X_1X_2\) and \(V=X_2\).

\textbf{(b)} Find the marginal pdf of \(U\).

Topic Tags

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