A long-distance taxi service owns four vehicles. These are of different ages and have different repair records. The probabilities that, on any given day, each vehicle will be available for use are 0.95, 0.90, 0.90, and 0.80.
Whether one vehicle is available is independent of whether any other vehicle is available.
a. Find the probability distribution for the number of vehicles available for use on a given day.
b. Find the expected number of vehicles available for use on a given day.
c. Find the standard deviation of the number of vehicles available for use on a given day.