This chapter introduced the concept of time headway in traffic flow and proposed a particular distribution for X = the headway between two randomly selected consecutive cars (sec). Suppose that in a different traffic environment, the distribution of time headway has the form below. f(x)={ k/x^4 where x>1 and 0 where 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 is between 2 and 3 sec.
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?