Question

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. Find the joint probability function for Y1 and Y2.

Answer 1

P(Y1,Y2) = P(Y1=y1 and Y2=y2) where (y1=y2=0,1,2)

Explanation:

Probability is all about understanding. P represents the probability of an event e.g. the probability that Y1 is 1, that is, the probability that the number of contracts assigned to firm A is 1.

The lower case symbols y1 and y2 represents the particular number of contracts in each experiment.

It will be zero if we're testing for the probability of either Y1 or Y2 being zero.

So, there are 3 events or possible outcomes for firm A:

1. They get no contract (y1=0)

2. They get one contract (y1=1)

3. They get the two contracts (y1=2)

These 3 events are also possible outcomes for firm B

Hence the function above embodies all this probability information.

I hope you understood my explanation.