1. The cafeteria in a building offers three different lunches. The demands for the three types of lunch on any given day are independent and Poisson distributed with means 4.85, 12.70, and 27.61. The cost of the three types are $12.00, $8.50, and $6.00, respectively. Find the expected value and variance of the total cost of lunches bought on a particular  day.

2. The mean time between failures (MTBF) of a hydraulic press is to be estimated assuming that the time between failures (TBF) is exponentially distributed. A foreman observes that the chance that the TBF is more than 72 hours is 50%, and he quotes 72 hours as the MTBF.

a. Is the foreman right? If not, what is the MTBF?

b. If the MTBF is indeed 72 hours, 50% of the time the TBF will be more than how many hours?

c. Why is the mean of an exponential distribution larger than its median?