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For X = 0, 1, 2, 3 10 10. Suppose We Have A Frequency Function For Two Variables X And Y. F(x,y) And

for x = 0, 1, 2, 3 10 10. Suppose we have a frequency function for two variables X and Y. f(x,y) and y=0,1,2. a. Determine the marginal distributions of X and Y. b. Determine E(X) and En. c. Determine ECX+Y. d. IfZ-2X+10, determine E(Z). e. Determine ECXY. f. Determine cov(x,). g. Are X and Y independent? Justify your answer.

a) From the given data, The marginal distribution of X and Y is X / Y 0 1 2 P(X=x) 0 0.000 0.033 0.067 0.100 1 0.033 0.067 0.100 0.200 2 0.067 0.100 0.133 0.300 3 0.100 0.133 0.167 0.4