answer all questions with explanation

Q1. "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. k f ( x) =- x12, if x>1 (a) Determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) (b) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.) (c) Find the probability density function (pdf) of Y = 2X. (Hint. Think about the relation between cdf and pdf.)