Annie and Alvie have agreed to meet for lunch between noon (o: oo p.m.) and 1:00 p.m. Denote Annie's arrival time by X, Alvie's by Y, and suppose X and Y are independent with pdf's fx ( x) = {3x 2 0

Annie and Alvie have agreed to meet for lunch between noon (o: oo p.m.) and 1:00 p.m. Denote Annie's arrival time by
X,
Alvie's byY,
and suppose
X
and
Yare independent with pdf's

fx<sup>(


x)</sup>
=
 {3x²
0
x

1

             0 otherwise

f y^(y)
=    { 2y²
0 < y=""><>

                  0 otherwise

What is the expected amount of time that the one who arrives first must wait for the other person?
[

Hint
:

h
(
X,
Y)
=

I

X

-
YI .]