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 next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form. f(x) = k/(x^7) ; 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 sex.
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?