3. (10 pts.) Suppose that a machine in a lab is operated by three types of people: students, professors, and intruders. If a student operates the machine, the amount of time spent on it (in minutes) is a random variable with uniform(0, 3) distribution. If a professor operates the machine, the time spent on it has exp(1) distribution. If an intruder operates the machine, the time spent on it is Rayleigh(1) distributed. Suppose that you are the lab manager, and you notice that someone operated the machine for 2 minutes this morning. a. Use the maximum-likelihood rule to decide who operated the machine this morning. b. Suppose that you know beforehand that the machine is operated by students 20% of the time, by professors 75% of the time, and by intruders 5% of the time. Use this information together with the MAP rule to decide who operated the machine this morning