# Question: let x y be two random variables with the...

###### Question details

) Let X, Y be two random variables with the following
properties. Y had

density function fY (y) = 3y

2

for 0 < y < 1 and zero elsewhere. For 0 < y < 1, given
Y = y, X

had conditional density function fX|Y (x | y) = 2x

y

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.