Question

"Time headway" in traffic flow is the elapsed time between the time moment when one car finishes passing a fixed point and the instant when the next car begins to pass that point. Let the random variable X be the time headway (in seconds) for two randomly chosen consecutive cars on a freeway during a period of heavy traffic flow. Suppose that in a particular traffic environment, the probability density function (pdf) of time headway X has the following form: a) Determine the value of k for which f(x) is a valid pdf. b) Obtain the cumulative distribution function (cdf) corresponding to the above pdf. c) Calculate the expected value of X and the standard deviation of X. d) What is the probability that X is within two standard deviations of its mean value?

Answer 1