Answered: IF F(x, y) is the value of the joint…

IF F(x, y) is the value of the joint distribution function of X and Y at (x, y), show that the marginal distribution function of X is given by G(x) = F(x, ∞) for - ∞ 0, y> 0 and 0 elsewhere

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 12CR

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Question

IF F(x, y) is the value of the joint distribution function of X and Y at (x, y), show that the marginal distribution function of X is given by

G(x) = F(x, ∞) for - ∞ <x < ∞

Use this result to find the marginal distribution function of X for the random variable

F(x, y) = { (1-e^{-x^2} ) (1- e^{-y^2}) for x>0, y> 0 and 0 elsewhere

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