Question: 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

You are given two discrete random variables X, Y that assume the possible values 0, 1 according to the following joint distribution:
align="center">You are given two discrete random variables X, Y that

(a) What are the marginal distributions of X and Y?
(b) Are X and Y independent?
(c) Calculate E[X] 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 V[X| Y = 1].

P(Y 1) P(Y 0) P(Y 1 0.2 P(Y 0) 0.15 0.4 0.25

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