Consider a machine which manufactures components. The machine operates for a random period of time T before it needs to be shut down for service. T is uniformly and continuously distributed between 0 and 4 days. If the machine has been operating for less than or equal to 2 days, it manufactures components according to a Poisson process with a rate of 1 components/day. If the machine has been operating for more than 2 days, the components are still manufactured according to a Poisson process, but the rate goes down to 2 components/day. A Poisson process indicates that the number of components manufactured in a given time frame is a random variable that follows the Poisson distribution. Express your answers in terms of 1 and 2. You do not need to simplify integrals or summations. (a) Find the expected number of components manufactured while the machine is operating. (b) Find the probability that 0 components are manufactured during the time that the machine is operational. (c) Find the probability that exactly 1 component is manufactured during the time that the machine is operational.