Question

3. (Anderson, 10.7) Let X, Y be two random variables with the following properties, Y had density function fr (y-3/ for 0 < y < 1 and zero elsewhere. For 0 < y < 1, given Y y.x had conditional density function fxy )for0 <y and zero elsewhere. (a) Find the joint density function fx.y. Be precise about where the values (a, ) are non-zero. Check that the joint density function integrates to 1. (b) Find the conditional density function of Y givenX a

) 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.

Answer 1