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(c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) 0.00048 0.0005 Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) 0.0002 x 0.0005 (d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) 1.2 X 1.1 mean standard deviation 0.539 X 0.111 (e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.) 896.4426 X 0.878

(c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) 0.00048 0.0005 Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) 0.0002 x 0.0005 (d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) 1.2 X 1.1 mean standard deviation 0.539 X 0.111 (e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.) 896.4426 X 0.878

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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I need help with parts “c”, “d, and “e” thanks.
"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. 0 xs1 (a) Determine the value of k for which f(x) is a legitimate pdf. 11✔ 11 (b) Obtain the cumulative distribution function. F(x) = x>1 0 mean (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) 0.0005 0.00048✔✔ Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) 0.0005 0.0002 x standard deviation x>1 (d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) 1.2 X 1.1 xs1 0.539 X 0.111 (e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.) 896.4426 X 0.878
Transcribed Image Text:"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. 0 xs1 (a) Determine the value of k for which f(x) is a legitimate pdf. 11✔ 11 (b) Obtain the cumulative distribution function. F(x) = x>1 0 mean (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) 0.0005 0.00048✔✔ Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) 0.0005 0.0002 x standard deviation x>1 (d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) 1.2 X 1.1 xs1 0.539 X 0.111 (e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.) 896.4426 X 0.878
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