"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< 1a) determine the value of k for which f(x) is a legitimate pdfb) obtain the cumulative distribution functionf(x) = [ blank ] ; x > 1 0 ; x < 1c) use the cdf from (b) to determine the probability that headway exceeds 2 sex. (round your answer to three decimal places.)use the cdf from (b) to determine the probability that headway is between 2 and 3 sec (round your answer to three decimal places)d) obtain the mean value of headway and the standard deviation of headway. (roun to nearest 3 decimal places)mean [ blank ]standard deviation [ blank ]e) what is the probability that headway is within 1 standard deviation of the mean value?