8. A pair of jointly continuous random variables, X and Y have the joint density 10 function uniform distributed over 1/2
8. A pair of jointly continuous random variables, X and Y have the joint density 10 function uniform distributed over 1/2
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.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 44CR
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![8. A pair of jointly continuous random variables, X and Y have the joint density 10
function uniform distributed over 1/2<x+y<1, if 0 < x, y ≤1 and 0 elsewhere.
(a) Find the PDF, fxy(x, y).
(b) Find the marginal PDFs of X and Y, i.e. fx (x) and fy (y).
(c) Find E[XY ] and Var[X]
(d) Find the conditional PDF for X given that Y3/4, i.e., Jxy (2|3/4).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd2d1959-46ea-4e22-9d0f-1ad88e6676e4%2Fc579ac10-448a-479e-b7e9-4216a88282c7%2Fb61mtf_processed.png&w=3840&q=75)
Transcribed Image Text:8. A pair of jointly continuous random variables, X and Y have the joint density 10
function uniform distributed over 1/2<x+y<1, if 0 < x, y ≤1 and 0 elsewhere.
(a) Find the PDF, fxy(x, y).
(b) Find the marginal PDFs of X and Y, i.e. fx (x) and fy (y).
(c) Find E[XY ] and Var[X]
(d) Find the conditional PDF for X given that Y3/4, i.e., Jxy (2|3/4).
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