'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 be the time headway for two randomly chosen consecutive cars (in seconds). Suppose X has pdf f(x) {* F(x) (a) Find the value of k. (b) Obtain the mean value of headway and the standard deviation of headway. (c) The cdf of X is = x > 1 x ≤ 1 0 1- x ≤ 1 x>1 Using the cdf, determine the following probabilities. (i) What is the probability that observed depth is at most 3? (ii) What is the probability that observed depth is between 3 and 2?
'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 be the time headway for two randomly chosen consecutive cars (in seconds). Suppose X has pdf f(x) {* F(x) (a) Find the value of k. (b) Obtain the mean value of headway and the standard deviation of headway. (c) The cdf of X is = x > 1 x ≤ 1 0 1- x ≤ 1 x>1 Using the cdf, determine the following probabilities. (i) What is the probability that observed depth is at most 3? (ii) What is the probability that observed depth is between 3 and 2?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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Transcribed Image Text:'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 be the time headway for two randomly chosen
consecutive cars (in seconds). Suppose X has pdf
f(x)
=
{*
F(x)
(a) Find the value of k.
(b) Obtain the mean value of headway and the standard deviation of headway.
(c) The cdf of X is
=
x > 1
x ≤ 1
0
1-
x ≤ 1
x>1
Using the cdf, determine the following probabilities.
(i) What is the probability that observed depth is at most 3?
(ii) What is the probability that observed depth is between 3 and 2?
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