Problem #3 (20 points) - A Reliability Problem A certain component of a machine has a lifetime that is exponentially dis

tributed with a mean of 10 hours. When this component fails, the machine

is stopped and the component must be replaced. Suppose that the replace—

ment time is uniformly distributed between 25 and 35 minutes. In addition,

company policy is to replace the component after 15 hours of operation even

if it has not failed. Run 10 simulations to mimic the replacement of 100 such

components. Use your simulations to determine: a.) (5 points) the average total time of the simulation, b.) (5 points) the average number of components that must be replaced during

the ﬁrst ﬁve days of operation, c.) (5 points) the average time (in hours) that a component is used, and

d.) (5 points) the average percent of the time the machine is idle. Hint: You may use the fact that a sample X from an exponential dis- tribution with mean a can be computed from a random number R using

X = —aln(R).