Example 4.5 introduced the concept of time headway in traffic flow and proposed a particular distribution for

Question:

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

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?

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...