13. Example 4.5 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 f(x)


k x4 x 1 0 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 exceeds 2 sec and also 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?