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Mathematics, 10.03.2020 04:30 cassandrabeliles

Example 4.5 introduced the concept of time headway in traffic flow and proposed a particular distribution for X 5 the headway between two randomly selected consecutive cars (sec). Suppose that in a different traffic environment, the distribution of time headway has the form f(x) 5 5 k x4 x . 1 0 x # 1 a. Determine the value of k for which f (x) is a legitimate pdf. b. Obtain the cumulative distribution function. c. Use the cdf from (b) to determine the probability that headway exceeds 2 sec and also the probability that headway is between 2 and 3 sec. d. Obtain the mean value of headway and the standard deviation of headway. e. What is the probability that headway is within 1 standard deviation of the mean value?

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