Suppose that X and Y are random variables with a joint densi

Suppose that X and Y are random variables with a joint density f(x,y) = {2/5(2x + 3y), when 0

Solution

fx(X) = integral 2/5(2x+3y) dy

= 2/5(2xy + 3y^2/2)

fy(Y) = integral 2/5(2x+3y) dx

= 2/5(x^2 + 3yx)

Distribution of 2X+3Y = 2 * 2/5(2xy + 3y^2/2) + 3 * 2/5(x^2 + 3yx)

= 2/5 (4xy + 3y^2 + 3x^2 + 9xy)

= 2/5 ( 3x^2 + 13xy + 3y^2) Answer