A local pharmacy has two checkout stations available to its customers: a regular checkout station and an

Question:

A local pharmacy has two checkout stations available to its customers: a regular checkout station and an express checkout station. Customers with six or fewer items are assumed to join the express line. Let X and Y be the numbers of customers in the regular checkout line and the express checkout line, respectively, at the busiest time of a typical day. Note that these numbers include the customer(s) being served, if any. The joint for X and Y is given in the file S04_30.xlsx.
a. Find the marginal distributions of X and Y. What does each of these distributions tell you?
b. Find the conditional of X given Y. What is the practical benefit of knowing this conditional
c. What is the probability that no one is waiting or being served in the regular checkout line?
d. What is the probability that no one is waiting or being served in the express checkout line?
e. What is the probability that no more than two customers are waiting in both lines combined?
f. On average, how many customers would you expect to see in each of these two lines during the busiest time of day at the pharmacy?

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...