Refer to Exercise 4.109. Find an interval that will

Chapter 4, Problem 152E

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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.

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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

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