A toll bridge over the River Jay is operated by a private company who are thinking of installing automatic machines to collect the tolls. These machines,
however, are not perfectly reliable and it is thought that the number of breakdowns occurring per day would follow the probability distribution shown
below:

When a breakdown occurred, revenue from tolls would be lost until the equipment was repaired. Given below are approximate probability distributions for the
equipment repair time and the average revenue lost per hour.

(a) Determine the probability distribution of revenue which would be lost per day as a result of machine breakdowns (it can be assumed that the above
probability distributions are independent).

(b) Calculate the expected loss of revenue per day and interpret your result.