The joint probability density function of a pair continuous random variables X and Y is given by k(6-x-y) for 0

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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The joint probability density function of a pair continuous random variables X and Y is
given by
k(6-x-y) for 0<x<2, 2< y < 4
f(x, y)
==
elsewhere
(a) Show that k½ for which f(x, y) is a joint probability density.
(b) Find the marginal density of Y.
(c) Find the conditional density of X given Y=y, and use it to evaluate
P(X ≤1.5|Y
3.5).
Transcribed Image Text:The joint probability density function of a pair continuous random variables X and Y is given by k(6-x-y) for 0<x<2, 2< y < 4 f(x, y) == elsewhere (a) Show that k½ for which f(x, y) is a joint probability density. (b) Find the marginal density of Y. (c) Find the conditional density of X given Y=y, and use it to evaluate P(X ≤1.5|Y 3.5).
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