(Solved): show all steps and solve all parts thank you <3 period of heavy flow (sec). Suppose that in a par ...

period of heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form. $f(x)=\{\begin{array}{cc}\frac{k}{x^{10}}& x>1\\ 0& x\le 1\end{array}$ (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 sec. (Round your answer to four decimal places.) Use the cdf from (b) to determine the probability that headway is between 2 and $3\sec$. (Round your answer to four decimal places.) (d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) mean standard deviation (e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.)