"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 consecutivecars 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.kx > 1f(x):.10X < 1(a) Determine the value of k for which f(x) is a legitimate pdf.(b) Obtain the cumulative distribution function.x > 1F(x)X < 1(c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.)Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.)(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.)

Since the question has multiple sub parts we will solve the first part only. Please resend the…

x >1 f(x) =x10 xs1 ermine the value of k for which f(x) is a legitimate pdf. ain the cumulative distribution function. x > 1 xs1 the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) ain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) n dard deviation it is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.)

x >1 f(x) =x10 xs1 ermine the value of k for which f(x) is a legitimate pdf. ain the cumulative distribution function. x > 1 xs1 the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) ain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) n dard deviation it is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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