Need help with unanswered portions "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.9.(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.)

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OObtain the cumulative distribution function. x > 1 F(x) xs1 OUse 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.)

OObtain the cumulative distribution function. x > 1 F(x) xs1 OUse 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.)

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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"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
x > 1
f(x)
10
X < 1
(a) Determine the value of k for which f(x) is a legitimate pdf.
9.
(b) Obtain the cumulative distribution function.
x > 1
F(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.)

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