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# Contracts for two construction jobs are randomly assigned ISBN: 9780495110811 47

## Solution for problem 1E Chapter 5

Mathematical Statistics with Applications | 7th Edition

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Problem 1E

Contracts for two construction jobs are randomly assigned to one or more of three firms, A, B, and C. Let Y1 denote the number of contracts assigned to firm A and Y2 the number of contracts assigned to firm B. Recall that each firm can receive 0, 1, or 2 contracts.

a Find the joint probability function for Y1 and Y2.

b Find F(1, 0).

Step-by-Step Solution:

Step 1 of 2:

(a)

The contract for two construction jobs are randomly assigned to one or more of three firms, Let denote the number of contracts assigned to firm and the number of contracts assigned to firm Recall that each firm can receive contracts.

We need to find the joint probability function for and Let and be discrete random variables. The joint (or bivariate) probability function for and is given by, …………(1)

Let denote the pair of event that contracts are assigned to firm and contracts are assigned to firm Here can take values since there are only two construction jobs.

To find the total number of events in the sample space, we need to find out the number of pairs.

So by the product rule, a total number of ways is Therefore the sample space  Hence the probability that contracts is assigned to firm and 0  contracts assigned to firm Using equation (1),  [ ] Similarly, we can write,      Similarly, we can write the probability,      Lets update the above values in the joint table.

Hence the joint distribution of  \ 0 1 2 Total 0    1  0 2 0 0 Total   1

Step 2 of 2

##### ISBN: 9780495110811

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