XA Washington DC commuter must take two Metro trains to get to work. This involves a wait time T, for the first train and a wait time T, for the second train. The total wait time (in minutes) T = T, + T2 has a pdf given by 0st<4 16 f(t) = {1 1 -t 16 4sts8 t< 0 and t > 8 a) Compute the cdf. b) Compute the 75'th percentile. c) Compute E (t). d) Compute E(t²). e) What is the probability that the total wait time is within 1 standard deviation of the mean.
XA Washington DC commuter must take two Metro trains to get to work. This involves a wait time T, for the first train and a wait time T, for the second train. The total wait time (in minutes) T = T, + T2 has a pdf given by 0st<4 16 f(t) = {1 1 -t 16 4sts8 t< 0 and t > 8 a) Compute the cdf. b) Compute the 75'th percentile. c) Compute E (t). d) Compute E(t²). e) What is the probability that the total wait time is within 1 standard deviation of the mean.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Transcription for Educational Website**
A Washington DC commuter must take two Metro trains to get to work. This involves a wait time \( T_1 \) for the first train and a wait time \( T_2 \) for the second train. The total wait time (in minutes) \( T = T_1 + T_2 \) has a probability density function (pdf) given by
\[
f(t) =
\begin{cases}
\frac{1}{16} t & 0 \leq t < 4 \\
\frac{1}{2} - \frac{1}{16} t & 4 \leq t \leq 8 \\
0 & t < 0 \text{ and } t > 8
\end{cases}
\]
Tasks:
a) Compute the cumulative distribution function (CDF).
b) Compute the 75th percentile.
c) Compute \( E(t) \).
d) Compute \( E(t^2) \).
e) What is the probability that the total wait time is within 1 standard deviation of the mean?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8edd889e-338a-4275-872c-5b2b400b4e22%2F6336d66a-4060-4682-87d7-a489e563b0a0%2F6zb06c6_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website**
A Washington DC commuter must take two Metro trains to get to work. This involves a wait time \( T_1 \) for the first train and a wait time \( T_2 \) for the second train. The total wait time (in minutes) \( T = T_1 + T_2 \) has a probability density function (pdf) given by
\[
f(t) =
\begin{cases}
\frac{1}{16} t & 0 \leq t < 4 \\
\frac{1}{2} - \frac{1}{16} t & 4 \leq t \leq 8 \\
0 & t < 0 \text{ and } t > 8
\end{cases}
\]
Tasks:
a) Compute the cumulative distribution function (CDF).
b) Compute the 75th percentile.
c) Compute \( E(t) \).
d) Compute \( E(t^2) \).
e) What is the probability that the total wait time is within 1 standard deviation of the mean?
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