Question: A scientist has a machine for measuring ozone in the atmosphere that is located in the mountains just north of Los Angeles. At times of

A scientist has a machine for measuring ozone in the atmosphere that is located in the mountains just north of Los Angeles. At times of a Poisson process with rate 1, storms or animals disturb the equipment so that it can no longer collect data. The scientist comes every L units of time to check the equipment.

If the equipment has been disturbed then she can usually fix it quickly so we will assume the repairs take 0 time.

(a) What is the limiting fraction of time the machine is working?

(b) Suppose that the data that is being collected is worth a dollars per unit time, while each inspection costs c <

a. Find the best value of the inspection time L.

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