Vending machine. The time between consecutive uses of a vending machine is Exponential with average 15 minutes.
a. Given that the machine has not been used in the previous 5 minutes, what is the probability that the machine will not be used during the next 10 minutes?
b. How many purchases are expected within the next hour?
c. What is the distribution of the number of purchases to be made within the next hour?
d. Suppose that a person pays 75 cents for each beverage in the vending machine. The supplier pays 40 cents per beverage in the machine, and thus makes a profit of 35 cents per beverage. What is the expected profit made during a given 8 hour period?