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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2015 • Question 3

Question

Math 6010 • Linear Models Spring 2015 • Question 3

Let \(X\) and \(Y\) be independent random variables. Show that if the distribution of \(X\) is absolutely continuous with respect to the Lebesgue measure, then the distribution of \(X+Y\) is also absolutely continuous with respect to the Lebesgue measure.

Raw LaTeX

Let \(X\) and \(Y\) be independent random variables. Show that if the
distribution of \(X\) is absolutely continuous with respect to the Lebesgue
measure, then the distribution of \(X+Y\) is also absolutely continuous with
respect to the Lebesgue measure.

Topic Tags

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