"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 fo two randomly chosen consecutive cars on a freeway during a period of heavy flow. The pdf of X is the following. 0.17e-0.17(x - 0.5) 0 x ≥ 0.5 otherwise (a) What is the probability that time headway is at most 6 sec? (Round your answer to three decimal places.) f(x) = = {0.17e-0 (b) What is the probability that time headway is more than 6 sec? At least sec? (Round your answers to three decimal places.) more than 6 sec. at least 6 sec (c) What is the probability that time headway is between 5 and 6 sec? (Round your answer to three decimal places.)
"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 fo two randomly chosen consecutive cars on a freeway during a period of heavy flow. The pdf of X is the following. 0.17e-0.17(x - 0.5) 0 x ≥ 0.5 otherwise (a) What is the probability that time headway is at most 6 sec? (Round your answer to three decimal places.) f(x) = = {0.17e-0 (b) What is the probability that time headway is more than 6 sec? At least sec? (Round your answers to three decimal places.) more than 6 sec. at least 6 sec (c) What is the probability that time headway is between 5 and 6 sec? (Round your answer to three decimal places.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![**Time Headway in Traffic Flow**
"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 \( X \) represent the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow. The probability density function (pdf) for \( X \) is given as follows:
\[
f(x) =
\begin{cases}
0.17 e^{-0.17(x - 0.5)} & \text{for } x \geq 0.5 \\
0 & \text{otherwise}
\end{cases}
\]
**Questions**
(a) What is the probability that time headway is at most 6 seconds? (Round your answer to three decimal places.)
[Input field for answer]
(b) What is the probability that time headway is more than 6 seconds? Also, find the probability that it is at least 6 seconds. (Round your answers to three decimal places.)
Probability that it is more than 6 seconds: [Input field]
Probability that it is at least 6 seconds: [Input field]
(c) What is the probability that time headway is between 5 and 6 seconds? (Round your answer to three decimal places.)
[Input field for answer]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc02cea10-2b20-4726-bfe2-8f9101f448fb%2Fff8a4672-4f78-4458-af59-ec0bb0511002%2Ftpn9pj_processed.png&w=3840&q=75)
Transcribed Image Text:**Time Headway in Traffic Flow**
"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 \( X \) represent the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow. The probability density function (pdf) for \( X \) is given as follows:
\[
f(x) =
\begin{cases}
0.17 e^{-0.17(x - 0.5)} & \text{for } x \geq 0.5 \\
0 & \text{otherwise}
\end{cases}
\]
**Questions**
(a) What is the probability that time headway is at most 6 seconds? (Round your answer to three decimal places.)
[Input field for answer]
(b) What is the probability that time headway is more than 6 seconds? Also, find the probability that it is at least 6 seconds. (Round your answers to three decimal places.)
Probability that it is more than 6 seconds: [Input field]
Probability that it is at least 6 seconds: [Input field]
(c) What is the probability that time headway is between 5 and 6 seconds? (Round your answer to three decimal places.)
[Input field for answer]
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