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Refer to Exercise 4.109. Find an interval that will
Chapter 4, Problem 152E(choose chapter or problem)
Problem 152E
Refer to Exercise 4.109. Find an interval that will contain L for at least 89% of the weeks that the machine is in use.
Reference
The weekly amount of downtime Y (in hours) for an industrial machine has approximately a gamma distribution with α = 3 and β = 2. The loss L (in dollars) to the industrial operation as a result of this downtime is given by L = 30Y + 2Y 2. Find the expected value and variance of L.
Questions & Answers
QUESTION:
Problem 152E
Refer to Exercise 4.109. Find an interval that will contain L for at least 89% of the weeks that the machine is in use.
Reference
The weekly amount of downtime Y (in hours) for an industrial machine has approximately a gamma distribution with α = 3 and β = 2. The loss L (in dollars) to the industrial operation as a result of this downtime is given by L = 30Y + 2Y 2. Find the expected value and variance of L.
ANSWER:
Solution :
Step 1 of 1:
Our goal is:
We need to find an interval that will contain L for at least 89% of the weeks that the machine is in use.
Let Y have a gamma distribution with =3 and =2.
Here loss L=30Y+2
We know that from