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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. x> 1 x≤1 (a) Determine the value of k for which f(x) is a legitimate pdf. f(x) = x12 (b) Obtain the cumulative distribution function. F(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.) Use the cdf from (b) to determine the probability that headway is between 2 and sec. (Round your answer to four decimal places.) standard deviation (d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) mean (e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.)

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. x> 1 x≤1 (a) Determine the value of k for which f(x) is a legitimate pdf. f(x) = x12 (b) Obtain the cumulative distribution function. F(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.) Use the cdf from (b) to determine the probability that headway is between 2 and sec. (Round your answer to four decimal places.) standard deviation (d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) mean (e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.CR: Chapter 2 Review
Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...
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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. f(x) = (a) Determine the value of k for which f(x) is a legitimate pdf. F(x) = k x12 0 (b) Obtain the cumulative distribution function. 0 x > 1 x ≤ 1 mean x > 1 (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) x ≤ 1 Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) standard deviation (d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) (e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.)
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. f(x) = (a) Determine the value of k for which f(x) is a legitimate pdf. F(x) = k x12 0 (b) Obtain the cumulative distribution function. 0 x > 1 x ≤ 1 mean x > 1 (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) x ≤ 1 Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) standard deviation (d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) (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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