Question

Roll a pair of fair dice. Let X be the number of ones in the outcome and let Y be the number of twos in the outcome. Find E[XY].

Answer 1

E(XY)=1/18

Explanation:

x y P(x,y) xy*P(X,Y)

0 0 4/9 0

0 1 2/9 0

1 0 2/9 0

1 1 1/18 1/18

2 0 1/36 0

0 2 1/36 0

1 1/18

from above:

E(XY)=1/18