Solution: Example 4.5 introduced the concept of time headway
Chapter 4, Problem 4.21(choose chapter or problem)
Example 4.5 introduced the concept of time headway in traffic flow and proposed a particular distribution for X 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) 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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