You are given two discrete random variables X. Y that assume the possible values 0, 1 according to the following joint distribution:

(a) What are the marginal distributions of X and Y?(b) Are x and Y independent?(e) Calculate E[1] and E[Y].(d) Calculate the conditional distribution P[X|Y = 1].(e) Obtain the conditional expectation E [X| Y = 1] and the conditional variance Var[X|Y =1].

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P(Y = 1) P(Y = (0) %3D P(X=1) .2 P(X=0) .15 .25