• Let the breakdown of a machine follow the Poisson process so that the random variable X denoting the number of breakdowns per unit of time is distributed as a Poisson distribution. Then, the time between any two consecutive failures is also a random variable T that is distributed as an exponential with parameter . If =0.1, what is the probability that the machine will function from 2 to 5 hours before it breaks down again?

• From a given data set on lifetime T of a certain system, the parameters of a Weibull distribution are estimated to be =4 and =0.5, where t is measured in thousands of hours with =0. What is P(T10)?