1.- The optimal scheduling of preventative maintenance tests of some (but not all) of n independently operating components was developed in Reliability Engineering and System Safety (January 2006). The time (in hours) between failures of a component was approximated by an exponential distribution with mean 0. a. Suppose 0=1,000 hours. Find the probability that the time between component failures ranges between 1,200 and 1,500 hours. b. Again, assume 0=1,000 hours. Find the probability that the time between component failures is at least 1,200 hours. c. Given that the time between failures is at least 1,200 hours, what is the probability that the time between failures is less than 1,500 hours?