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. (30 points) Cars arrive at a railroad crossing according to a Poisson process with rate A > 0. Due to a train passing by, the crossing is blocked for a random length of time that is exponentially distributed with parameter u > 0. Assume that the arrival process of cars and the length of time that the crossing is blocked are independent. (a) What is the probability that no cars arrive while the crossing is blocked? (b) What is the probability that three or more cars are waiting when the crossing is re-opened? (c) What is the expected number of cars waiting when the crossing is re-opened