Summary: Some worked problems from the Chapter Six homework.
p. 292 n. 20. In the first case X and Y are independent because the joint density factors; in fact,
fX(x) =
xe-x
if x > 0,
0 else
and fY (y) =
e-y
if y > 0,
0 else.
In the second case, X and Y are not independent because the set {(x, y) : 0 < x < y and 0 < y < 1} where
fX,Y is not zero is not a product.
p. 292 n. 22.
(a) No, the joint density fX,Y does not factor.
(b)
fX (x) =

0
fX,Y (x, y) dy =
1

Source: Allard, William K. - Department of Mathematics, Duke University

Collections: Mathematics