Probability and distribution on stat 235

30 "Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the nerd car begins to pass that point Let X be the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow (in seconds). Suppose that in a particular traffic environment, the distribution of time headway has the following form Az) = 0 After determining the value of k for which for) is a legitimate continuous random variable, what is the variance of headway? 0 10 91 141 F 9 1.25 Ti . 0.0154 . 0.124