QNB branch at QU has two cashier lines one of which is known

QNB branch at QU has two cashier lines, one of which is known to be faster than the other. Let X1 denotes the number of customers in the first line and X2 denotes the number of customers in the fast line at the same time of the day. Suppose the joint p.m.f. of X1 and X2 is given by the picture

1. What is the probability that both lines are empty?

2. What is the probability that both lines have the same length (i.e. same number of customers)?

3. What is the probability that the total number of customers in the two lines is exactly four?

4. What is the probability that the total number of customers in the two lines is at least four?

5. Find the marginal distribution of , , and expected value of ,

6. Find

7. Are X1 and X2 independent? Explain.

8. Calculate and Comment the Covariance of X1 and X2

Solution