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

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter2: Exponential, Logarithmic, And Trigonometric Functions

Section2.CR: Chapter 2 Review

Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...

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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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