In: Statistics and Probability
"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form.
f(x) =
|
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.
F(x) =
x > 1 | ||
0 | x ≤ 1 |
(c) Use the cdf from (b) to determine the probability that headway
exceeds 2 sec. (Round your answer to three decimal places.)
Use the cdf from (b) to determine the probability that headway is
between 2 and 3 sec. (Round your answer to three decimal
places.)
(d) Obtain the mean value of headway and the standard deviation of
headway. (Round your answers 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.)
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