Question: let x y be two random variables with the...
) Let X, Y be two random variables with the following
properties. Y had
density function fY (y) = 3y
for 0 < y < 1 and zero elsewhere. For 0 < y < 1, given Y = y, X
had conditional density function fX|Y (x | y) = 2x
2 for 0 < x < y and zero elsewhere.
(a) Find the joint density function fX,Y . Be precise about where the values (x, y) are non-zero.
Check that the joint density function integrates to 1.
(b) Find the conditional density function of Y given X = x.