5. Let X and Y be discrete random variables with Sx {0, 1, 2} and Sy = {0, 1, 2,3}. Define the joint probability mass function (x, y,) = P(X = x.Y = y) as follows: { x+y 30 x = 0, 1, 2 and y = 0, 1, 2, 3 f(x, y) otherwise a. Find the marginal distribution of X. That is to say find fx(x) = P(X = x) for x=0,1,2. b. Find the marginal distribution of Y. That is to say find fy(Y) = P(Y = Y) for y=0,1,2,3. c. Are X and Y independent random variables? (hint: check if f(x, y) = fx(x)fy(y))

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