Solution Found!
Refer to Exercise 4.129. Find an interval for which the
Chapter 4, Problem 153E(choose chapter or problem)
Refer to Exercise 4.129. Find an interval for which the probability that 𝐶 will lie within it is at
least .75.
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:
Refer to Exercise 4.129. Find an interval for which the probability that 𝐶 will lie within it is at
least .75.
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 1:
Our goal is:
We need to find an interval for which the probability that C will lie within it is at least 0.75.
Now we have to find an interval for which the probability that C will lie within it is at least 0.75.
Let Y have a beta distribution with =1 and
=2.