"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. f(x) = k x6 x > 1 0 x ≤ 1 (a) Determine the value of k for which f(x) is a legitimate pdf. 5 Correct: Your answer is correct. (b) Obtain the cumulative distribution function. F(x) = Correct: Your answer is correct. x > 1 0 x ≤ 1 (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to three decimal places.) 0.031 Correct: Your answer is correct. Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to three decimal places.) Incorrect: Your answer is incorrect. (d) Obtain the mean value of headway and the standard deviation of headway. (Round your answers to three decimal places.) mean standard deviation (e) What is the probability that headway is within 1 standard deviation of the mean value?