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Chapter 4 Practice Question 4 ii.

G

George Philip

Active Member
In he second part of this question, we take the mean/expected holding time in the broken state to be 0.25 days i.e on average ee stay in that state 6 hours a day.
And for the expected holding time in the working state, we take it to be 1 day. How did we induce this?
All we are given is that we "it tends to break down once a day".

Could some one explain how we arrived at this "1".

Thank you.
 
Hello

We are meant to interpret this as the average time to break down being 24 hours.

Think about it from say the perspective of a Poisson process counting potential break downs (potential as in reality it has to get fixed once broken down so it can't have multiple). We're told that the rate of break down per 24 hour period is 1, so the number of potential break downs in a 24 hour period could be modeled as a Poi(1) RV. The waiting time between break downs therefore has an Exp(1) distribution with mean 1/1 = 1. So the expected time between break downs is 1.

Hope this helps!

Andy
 
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