The time between process problems in a manufacturing line is exponentially distributed with a mean of 30 days.
Suppose that the problems can be classified into three mutually exclusive classes: I, II and III. The probability that a problem is of type I, II, and III, are respectively, 0.75, 0.2, 0.05. (i) Give the distribution of the waiting time for a process problem of type I. (ii) Suppose that the problems I, II and III, cost (per problem) $1,000; $2,500, $6,000, respectively. Give the mean total cost for process problems for a period of 90 days.