Two criminal cases/law suits are randomly assigned to one or more of three lawyers in a...

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Two criminal cases/law suits are randomly assigned to one or more of three lawyers in a big law firm: Anna, Ben and Cameron (abbreviated to A,B and C). Let X1 denote the number of contracts assigned to Anna and X2 denote the number of contracts assigned to Ben. For some reason, completely beyond my control, we are not interested in Cameron's escapades. 1. Find the joint probability function of X and X2. 2. Find the marginal distribution fx (1) of X and the marginal distribution fx2(x2) of X2. 3. Are X and Y independent? Give reasons. 4. Calculate the expected values E(X), E(Y) and the variances V ar(X), V ar(Y). 5. Calculate the covariance Cov(X1, X2) of X1 and X2. Hint: Use definition Cov(X,Y) = E[(X = E(X))(Y E(Y))](x E(X))(y E(y) * f(x, y)) z y Two criminal cases/law suits are randomly assigned to one or more of three lawyers in a big law firm: Anna, Ben and Cameron (abbreviated to A,B and C). Let X1 denote the number of contracts assigned to Anna and X2 denote the number of contracts assigned to Ben. For some reason, completely beyond my control, we are not interested in Cameron's escapades. 1. Find the joint probability function of X and X2. 2. Find the marginal distribution fx (1) of X and the marginal distribution fx2(x2) of X2. 3. Are X and Y independent? Give reasons. 4. Calculate the expected values E(X), E(Y) and the variances V ar(X), V ar(Y). 5. Calculate the covariance Cov(X1, X2) of X1 and X2. Hint: Use definition Cov(X,Y) = E[(X = E(X))(Y E(Y))](x E(X))(y E(y) * f(x, y)) z y