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.

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter2: Systems Of Linear Equations
Section2.4: Applications
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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
1
-t
16
0 st< 4
f(t) = {1
1
4 st<8
2 16
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.
Transcribed Image Text: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 1 -t 16 0 st< 4 f(t) = {1 1 4 st<8 2 16 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.
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