Question: 4. (8 points) The discrete integer-valued random variables X and Y have the joint probability mass function (PMF) Px,y(x, y) = P(X = x, Y

4. (8 points) The discrete integer-valued random variables X and Y

4. (8 points) The discrete integer-valued random variables X and Y have the joint probability mass function (PMF) Px,y(x, y) = P(X = x, Y = y) = clx + yl for re {-2, 0, 2}, ye {-1, 0, 1} and 0 otherwise. 1) (2 points) Find the value of the constant c. 2) (2 points) Find the expectation E(X ) and the variance var(X ). 3) (2 points) Find the covariance cov ( X, Y). 4) (2 points) Find the correlation coefficient px,y

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