The General Social Survey asked a sample of adults how many siblings (brothers and sisters) they had \((X)\) and also how many children they had \((Y)\). We show results for those who had no more than 4 children and no more than 4 siblings. Assume that the joint probability mass function is given in the following contingency table.

a. Find the marginal probability mass function of \(X\).

b. Find the marginal probability mass function of \(Y\).

c. Are \(X\) and \(Y\) independent? Explain.

d. Find \(\mu_{X}\) and \(\mu_{Y}\).

e. Find \(\sigma_{X}\) and \(\sigma_{Y}\).

f. Find \(\operatorname{Cov}(X, Y)\).
g. Find \(ho(X, Y)\).

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X 12340 2 O 0.03 0.09 0.09 0.06 0.04 y 1 0.01 0.02 0.05 0.08 0.05 0.07 0.04 0.07 0.03 0.04 2 3 0.01 0.03 0.04 0.04 0.03 4 0.01 0.01 0.02 0.02 0.02