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?

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )

pls refer ro the top for answer

df =

both have same length

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