You have purchased a light bulb. The box of the bulb states that the life time T of the product in years defined as P (T t) = e^t/4 for all t 0. (a) This is an example of a continuous probability model. Write down the sample space S (write it as an interval). (b) Make sure this is a valid probabilistic model by finding P (T 0) and limt P (T t). (c) Prove that if t1 < t2, then P (T t1) P (T t2). Why do you think this has to be true? (d) Find the probability that the product breaks down within four years of the purchase time. (e) Find the probability that the product breaks down in the second year, i.e., find P (1 T < 2).