Question

Please answer both parts of Question 1. Please show all work and all steps.

1.) In a room, there is a lightbulb with lifetime that is independently identically distributed with 4 months as the mean. A custodian enters to check the lightbulb at a rate 2 (per month) Poisson processes and will replace the lightbulb when it stops working.

a.) What is the rate for replacing the lightbulb?

b.) What is the limiting fraction of time that the light bulb can work?

Answer 1

We have given information:

Mean lifetime of the bulb (µ) = 4 months or 120 days

Lightbulb check rate (h) = 2 times per month or 24 times per year

We will perform the calculations by Considering 365 days in a year

A. The rate for replacing the lightbulb can be calculated as follows:

Rate of replacing the light bulb (Days) 365 Rate of replacing the light bulb (Days) =6120+242365= 27.02 days

B. The limiting fraction of time that light bulb can work can be calculated as: