4.

Flip a fair coin 4 times. Let X = number of heads, Y = 1 when the last flip is a tail. {a} Provide the joint distribution for X and Y. {b} Find E[X] and EFF]. {c} Find E[XY]. {d} Find the probability distribution fdr X |Y = 1. {e} Are X and Y independent? Suppose X and Y have the following joint distribution: XY -1 0.20 0.15 2 0.10 0.20 4 0.25 0.10 (a) Find the marginal distributions for X and Y. (b) Find E[X] and E[Y]. (c) Find P(X > 1). (d) Find E[XY]