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During an eight-hour shift, the proportion of time Y that
Chapter 4, Problem 129E(choose chapter or problem)
During an eight-hour shift, the proportion of time that a sheet-metal stamping machine is down for maintenance or repairs has a beta distribution with \(\alpha=1\) and \(\beta=2\). That is,
\(f(y)=\left\{\begin{array}{ll}
2(1-y), & 0 \leq y \leq 1, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
The cost (in hundreds of dollars) of this downtime, due to lost production and cost of maintenance and repair, is given by \(C=10+20 Y+4 Y^{2}\). Find the mean and variance of .
Equation Transcription:
Text Transcription:
alpha=1
beta=2
f(y)=
2(1-y), 0</=y</=1,
0, elsewhere.
C=10+20Y+4Y^2
Questions & Answers
QUESTION:
During an eight-hour shift, the proportion of time that a sheet-metal stamping machine is down for maintenance or repairs has a beta distribution with \(\alpha=1\) and \(\beta=2\). That is,
\(f(y)=\left\{\begin{array}{ll}
2(1-y), & 0 \leq y \leq 1, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
The cost (in hundreds of dollars) of this downtime, due to lost production and cost of maintenance and repair, is given by \(C=10+20 Y+4 Y^{2}\). Find the mean and variance of .
Equation Transcription:
Text Transcription:
alpha=1
beta=2
f(y)=
2(1-y), 0</=y</=1,
0, elsewhere.
C=10+20Y+4Y^2
ANSWER:
Solution:
Step 1 of 3:
It is given that Y denotes the proportion of time in an eight hour shift, a metal stamping machine is down for maintenance or repair.
Also, it is given that Y has a Beta distribution with parameters and
.
We have given with
f(y)=
Let C be the total cost of downtime and C=10+20Y+4.
We need to find the mean and variance of C.