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?