Assume we flip fair coin four times. Let X = number of heads, Y = 1 if last flip is a tails.
(a) Write down the joint distribution of X and Y .
(b) Find E[X] and E[Y ].
(c) Find E[XY ]
(d) Find the probability distribution for X|Y = 1.
(e) Are X and Y independent? Justify your answer.