Please be specific. Let the joint density function of random variables (X, Y) bef(x, y) =Ae-2x-3y,0,x>0, y > 0otherwise(1) Find the constant A;(2) Find the joint cumulative function of (X, Y);|(3) Calculate the following probabilities P(X + Y < 2), P(X > Y), P(X> 2Y|X> Y)(4) Are X and Y independent?

Given the joint density function of random variables :

Answered: Let the joint density function of…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 62CR

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Let the joint density function of random variables (X, Y) be f(x, y) = -2x-3y (Ae ²x-³y, x>0, y>0 0, otherwise (1) Find the constant A; (2) Find the joint cumulative function of (X, Y);| (3) Calculate the following probabilities P(X + Y < 2), P(X > Y), P(X > 2Y]\X> Y) (4) Are X and Y independent?