Question

2. The contracts for three independent construction jobs are to be assigned to one or more of four

competing firms: Firm A, Firm B, Firm C, and Firm D. For each contract, assume that it is equally

likely to be awarded to any of the four firms. Let X represent the number of contracts assigned to

Firm A, Y the number of contracts assigned to Firm B, and Z the number of contracts assigned

to Firm C.

(a) Determine the joint probability function of X and Y .

b) Calculate P(1 < T> 2) if T = X + Y + Z.

(c) Are X and Y independent random variables? Be sure to justify your response.

(d) The revenue Firm A generates (in dollars) from this assignment of jobs is given by the random

variable R = 300X2 + 175X + 25. What is the expected revenue for Firm A?

[5] (e) Calculate the correlation coefficient of X and Y . What can you say about the relationship

between X and Y ?

[4] (f) Calculate E(X - Y -Z) and Var(X - Y -Z).

[4] (g) In the next round of construction job assignments of which there are seven in total, sup-

pose that two of the contracts are acquired by Firm C. Given this information, what is the

probability that at least 3 of the contracts go to either Firm A or Firm B?