Show that the random variables with the densities f(x, y) = x + y and g(x, y) = (x + 1/2)(y + 1/2) if 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 and f(x, y) = 0 and g((x, y) = 0 elsewhere, have the same marginal distribution.

Chapter 24, PROBLEM SET 24.9 #19

Show that the random variables with the densities

f(x, y) = x + y

and

g(x, y) = (x + 1/2)(y + 1/2)

if 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 and f(x, y) = 0 and g((x, y) = 0 elsewhere, have the same marginal distribution.

Related Book For answer-question

Advanced Engineering Mathematics

10th edition

Authors: Erwin Kreyszig

ISBN: 978-0470458365