"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 nextcar begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavyflow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form.X > 10 x ≤ 1(a) Determine the value of k for which f(x) is a legitimate pdf.5f(x)(b) Obtain the cumulative distribution function.F(x)-51-x0X> 1x ≤ 1(c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.)0.0156xUse the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.)0.0271(d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.)meanstandard deviation(e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.)

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(a) Determine the value of k for which f(x) is a legitimate pdf. 5 (b) Obtain the cumulative distribution function. F(x) 1-x 0 X> 1 x≤ 1 (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) 0.0156 X Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) 0.0271

(a) Determine the value of k for which f(x) is a legitimate pdf. 5 (b) Obtain the cumulative distribution function. F(x) 1-x 0 X> 1 x≤ 1 (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) 0.0156 X Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) 0.0271

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 67E

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