Suppose X, Y have joint density function ƒ (x, y) = { # (xy + y²), 0≤x≤1 and 0≤y≤1 1 0, f otherwise. (a) Check that fis a genuine joint density function. (b) Find the marginal density functions of X and Y (c) Calculate the probability P(X

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Suppose X, Y have joint density function
f (x, y)
=
[¹/72 ( xy + y²), 0≤x≤ 1 and 0 ≤ y ≤1
0,
otherwise.
(a) Check that fis a genuine joint density function.
(b) Find the marginal density functions of X and Y
(c) Calculate the probability P (X<Y).
(d) Calculate the expectation E [X²Y].
Transcribed Image Text:Suppose X, Y have joint density function f (x, y) = [¹/72 ( xy + y²), 0≤x≤ 1 and 0 ≤ y ≤1 0, otherwise. (a) Check that fis a genuine joint density function. (b) Find the marginal density functions of X and Y (c) Calculate the probability P (X<Y). (d) Calculate the expectation E [X²Y].
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