Let X be the number of H that we obtain by flipping a fair coin 3 times and Y is the number of H that we obtain by flipping a not fair coin with p(H) = 4 times. a) Find the probability mass functions and the distribution functions of X and Y. b) Are X + Y and X.Y independent? Explain why or why not. c) Compute the expectation, the variance and the standard deviation of 2X + XY. d) Compute the covariance and the correlation of X and Y.

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