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"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form. k f(x) 6 x>1 X xs1 (a) Determine the value of k for which f(x) is a legitimate pdf. (b) Determine the probability that headway exceeds 2 sec. (Round your answer to five decimal places.) Determine the probability that headway is between 2 and 3 sec. (Round your answer to five decimal places.)