# Question

Two service elevators are used in parallel by employees of a three-story hotel building. At any point in time when both elevators are stationary, let X1 and X2 be the floor numbers at which elevators 1 and 2, respectively, are currently located. The joint probability distribution of X1 and X2 is given in the file S04_33.xlsx.

a. What is the probability that these two elevators are not stationed on the same floor?

b. What is the probability that elevator 2 is located on the third floor?

c. What is the probability that elevator 1 is not located on the first floor?

d. What is the probability that elevator 2 is located on the first floor; given that elevator 1 is not stationed on the first floor?

e. What is the probability that a hotel employee approaching the first-floor elevators will find at least one available for service?

f. Repeat part e for a hotel employee approaching each of the second- and third-floor elevators.

g. How might this hotel’s operations manager respond to your findings in the previous questions?

a. What is the probability that these two elevators are not stationed on the same floor?

b. What is the probability that elevator 2 is located on the third floor?

c. What is the probability that elevator 1 is not located on the first floor?

d. What is the probability that elevator 2 is located on the first floor; given that elevator 1 is not stationed on the first floor?

e. What is the probability that a hotel employee approaching the first-floor elevators will find at least one available for service?

f. Repeat part e for a hotel employee approaching each of the second- and third-floor elevators.

g. How might this hotel’s operations manager respond to your findings in the previous questions?

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