Multivariate Distributions 1. Contracts for two construction jobs are randomly assigned to one or more of three firms, A, B, and C. Let Y, denote the number of contracts assigned to firm A and Y2 the number of contracts assigned to firm B. Each firm can receive 0, 1, or 2 contracts. (a) Find the joint probability mass function for Y, and Y2. (b) Find F(1,0) (c) Find the marginal probability distribution of Y. (d) According what we know about distributions, Y, has a binomial distri- bution with n = 2 and p = 1/3. Is there any conflict between this result and the answer you provided in part (c)? 2. Continued from the previous question: (a) Are Y, and Y2 independent? (b) Find E(Y1 - Y2). (c) Find Cov(Y1, Y2). Provide intuition as to why this value is negative