Exercise 6.55 Let X and Y be random variables with joint density function if x, y > 0, f (x, y) = otherwise. Show that the joint density function of U = (X – Y) and V = Y is te -u-v if (u, v) E A, fu,v (u, v) = otherwise, where A is a region of the (u, v) plane to be determined. Deduce that U has the bilateral exponential distribution with density function fu (u) = ¿e-lu| for u e R.
Exercise 6.55 Let X and Y be random variables with joint density function if x, y > 0, f (x, y) = otherwise. Show that the joint density function of U = (X – Y) and V = Y is te -u-v if (u, v) E A, fu,v (u, v) = otherwise, where A is a region of the (u, v) plane to be determined. Deduce that U has the bilateral exponential distribution with density function fu (u) = ¿e-lu| for u e R.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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