The joint density function of the continuous variables X and Y is fX,Y(x,y) = (12/5)x(2-x-y) for...

Question

Question

The joint density function of the continuous variables X and Y is fX,Y(x,y) = (12/5)*x*(2-x-y) for 0<X<1 and 0<Y<1.

a) Find the expected value of X+Y.

(b) Find fX(x), and fY(y).

(c) Find Cov(X,Y).

(d) Find Corr(X,Y).

Answer 1

Answer #1

Solution: Let XRY have joint pot try (ny) = 2 x(2-8-47 dengan 6) Morginal pap of x fetary - 12 262-1-4) 9 - 12 x [2y-ay-2 to

ELY)= = E42) - 83 (34 gdy lzer & to + [5 ] ) (14) = 70 VOA )= F(42)-[E14)] = se =57-II do 1 a) f(x+y) = F(x)+E(4) < $ +} Elx

Answer 2

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The joint density function of the continuous variables X and Y is fX,Y(x,y) = (12/5)*x*(2-x-y) for...