Let X be the headway in seconds between two randomly selected consecutive car. Suppose that in a traffic environment, the distribution of X has the p.d.f. (a) Find the value of k. (b) Derive the c.d.f. F(x) of X. k f(x) == / for >1 (c) Use F(z) to obtain the probability that the headway is between 2 and 3 seconds. (d) Find E(X), the mean value headway.

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