When rolling a pair of dice, let X denote the number on the fi rst die, and Y the sum of the two dice. (a) Find E[X|Y = 5].(b) Find E[X|Y = y], for y = 2,....,12.(c) Compute (see attachment) which...

When rolling a pair of dice, let X denote the number on the first die, and Y the sum of the two dice.

(a) Find E[X|Y = 5].
(b) Find E[X|Y = y], for y = 2,....,12.
(c) Compute (see attachment) which should be equal to E[X] = 3.5.