Please answer letters d. and e. "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 aperiod of heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form.X> 1x ≤ 1(a) Determine the value of k for which f(x) is a legitimate pdf.11{f(x) =F(x) =(b) Obtain the cumulative distribution function.1111-meanx1200X > 1(c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.)0.0005x ≤ 1Use 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(d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.)standard 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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"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 ch period of heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form. f(x)=2 11 0 x51 (a) Determine the value of k for which f(x) is a legitimate pdf. (b) Obtain the cumulative distribution function. F(x)= x>1 1- 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.) 0.0005 Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) 0.0005 (d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) mean standard deviation (e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.)

"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 ch period of heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form. f(x)=2 11 0 x51 (a) Determine the value of k for which f(x) is a legitimate pdf. (b) Obtain the cumulative distribution function. F(x)= x>1 1- 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.) 0.0005 Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) 0.0005 (d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) mean standard deviation (e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 93E

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