"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
the two graph depicting proportional relationships are the top right and bottom left graphs
hope this helps and btw maybe make ur questions worth more points and dont make titles like this one lol also if its worth like 15 or more points put "__ POINTS"