'Example 4.5 introduced the concept of time headway in trafc flow and proposed a particular distribution for X = the headway beIWeen tWo randomly Selected Consecutive cars (sec). Suppose that in a different trafc environment, the distribution of time headway has the form k >1 x f(x)= X4 0 x5] a. Determine the value of k for which for) is a legiti- mate 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 see. (I. Obtain the mean value of headway and the standard deviation of headway. e. What is the probability that headway is within 1 stan dard deviation of the mean value