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Contracts for two construction jobs are randomly assigned to one or more of three firms, A, B, and C. LetY1denote the number of contracts assigned

Contracts for two construction jobs are randomly assigned to one or more of three firms, A, B, and C. LetY1denote the number of contracts assigned to firm A andY2the number of contracts assigned to firm B. Recall that each firm can receive 0, 1, or 2 contracts.

(a) Find the joint probability function forY1andY2.

(b) Find the marginal probability distribution ofY2.

(c) FindP(Y1= 1|Y21).

(d) FindE(Y1) andV(Y1).

(e) Find Cov(Y1, Y2).

(f) AreY1andY2independent? Explain!

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