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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2008 • Question 3

Question

Math 6010 • Linear Models Fall 2008 • Question 3

Let \(X\) and \(Y\) be two independent random variables with distribution functions \(F\) and \(G\) and density functions \(f\) and \(g\).

a. Determine the distribution function of \(XY\). (5 points)

b. Does \(XY\) always have a density function? (5 points)

c. Assuming that \(XY\) has a density function, compute it. (5 points)

Raw LaTeX

Let \(X\) and \(Y\) be two independent random variables with
distribution functions \(F\) and \(G\) and density functions \(f\) and \(g\).

a. Determine the distribution function of \(XY\). (5 points)

b. Does \(XY\) always have a density function? (5 points)

c. Assuming that \(XY\) has a density function, compute it. (5 points)

Topic Tags

Covariance and Independence Estimator Distributions Multivariate Normal Distributions Uniform Integrability and Truncation Methods