Question 6 Let X and Y be random variables such that X e {0, 1} and Y E {1, 2}. These are correlated such that3 P(X = 0 and Y = 1) = .1 P (X = 0 and Y = 2) = .3 P (X = 1 and Y = 1) = .4 P (X = 1 and Y = 2) = .2 (a) Calculate the (conditional) P(X = 0|Y = 1) and P(X = 1|Y =1) (b) Calculate the (unconditional) E [X], E [Y], and E [XY] (c) Calculate the (conditional) E [X | Y = 1] , E [X | Y = 2], and E [XY | Y = 1] (d) Calculate E [X | Y = 1 or Y = 2]