Suppose X and Y have joint PDFfX,Y (x, y) = cxy if 0 < x < y < 1                    0 otherwise.(Pay close attention to the support here.)a)  Find the value of c that makes this a valid joint PDF.b)  Find the marginal PDF of X.c)  Find the marginal PDF of Y .d)  Find the conditional PDF of Y given X = x. (This will be a function of bothx and y.)e) Are X and Y independent? Give a clear explanation for why or why not.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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 Suppose X and Y have joint PDF
fX,Y (x, y) = cxy if 0 < x < y < 1
                    0 otherwise.
(Pay close attention to the support here.)
a)  Find the value of c that makes this a valid joint PDF.
b)  Find the marginal PDF of X.
c)  Find the marginal PDF of Y .
d)  Find the conditional PDF of Y given X = x. (This will be a function of both
x and y.)
e) Are X and Y independent? Give a clear explanation for why or why not.

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