Question: Let for 0 x and 0 y. (a) Verify that f (x, y) is a valid density function. (b) Find themarginal density of

Let

f(x, y) = 2 (1+x+y)

for 0 · x and 0 · y.

(a) Verify that f (x, y) is a valid density function.

(b) Find themarginal density of X.

(c) Find E[Y ] , var[Y ], E[XY ] and corr(X,Y ).

(d) Find the conditional density of Y given X Æ x.

(e) Find E[Y j X Æ x].

f(x, y) = 2 (1+x+y)

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