You flip a fair coin twice. X is 2 if the first coin is headed and 4 if the first coin is tails. Y is 2 if the second coin is headed and 4 if the second coin is tails. Z is the product of X and Y where Z = XY. a) Calculate var(X + Y ).

b) Calculate Cov(X, Y ).

c) Calculate cov(Z, Y ).

d) Calculate E[Z|Y = 2].

e) Are X and Y independently distributed?

f) Are Z and Y independent?