4 Engineers often use the uniform distribution to model the arrival time of some event given that the event did occur within some interval. For example, pro- duction knows that a particular pump failed at some time between 1:00 and 3:00 P.M. Given that we know it failed at some time during this period, the pdf for the specific time within the period is f(y)= 0 otherwise where a = 1 and b = 3. This pdf essentially says that all the times within this interval are equally likely to occur. a. Derive the mean for this distribution. b. Derive the variance and the standard deviation for this distribution. c. Find the probability that the pump failed after 1:30 P.M.
4 Engineers often use the uniform distribution to model the arrival time of some event given that the event did occur within some interval. For example, pro- duction knows that a particular pump failed at some time between 1:00 and 3:00 P.M. Given that we know it failed at some time during this period, the pdf for the specific time within the period is f(y)= 0 otherwise where a = 1 and b = 3. This pdf essentially says that all the times within this interval are equally likely to occur. a. Derive the mean for this distribution. b. Derive the variance and the standard deviation for this distribution. c. Find the probability that the pump failed after 1:30 P.M.
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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Transcribed Image Text:4 Engineers often use the uniform distribution to model the arrival time of some
event given that the event did occur within some interval. For example, pro-
duction knows that a particular pump failed at some time between 1:00 and
3:00 P.M. Given that we know it failed at some time during this period, the pdf
for the specific time within the period is
f(y)=
0 otherwise
where a = 1 and b = 3. This pdf essentially says that all the times within this
interval are equally likely to occur.
a. Derive the mean for this distribution.
b. Derive the variance and the standard deviation for this distribution.
c. Find the probability that the pump failed after 1:30 P.M.
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