Chapter 5 - Question 5.17

[ljs84]

I am sure this is a really dumb question but in part ii) the generator matrix - how are the numbers 3/400, 1/400 and 1/25 calculated?

 

[johnpe21]

hi. any help with this one ?

 

[suraj]

hi. any help with this one ?

You have to multiply transition rate (1/20) with given probabilities.

A ---> M (Minor repair) = 1/20 * .15 = 3/400

A ---> S (Significant repair) = 1/20 * .05 = 1/400

A ---> H (Home sweet home) = 1/20 * .8 = 1/25

 

[johnpe21]

HI
Thanks for replying, but it seems that I still can't understand why we have to do this multiplication. Is it based on a formula in the notes that I can't figure out?

Shouldn't we calculate it based on the formula μij=nij/ti?

thanks a lot ..!

 

[suraj]

Is it based on a formula in the notes that I can't figure out?

No it is not based on any formula. These are just simple logic.

For example consider a Healthy-Sick-Dead model

suppose transitions out of HEALTHY state are occurring at the rate of 10
and after leaving healthy state,

probability of going to SICK state is 0.9 and probability of going to DEAD state is 0.1.
So we would expect people 9 people to go to SICK state and 1 to go DEAD state after a given time period.

That's why transition rate is multiplied with the probabilities.

Shouldn't we calculate it based on the formula μij=nij/ti?

This formula is used to estimate uij when it's not given. In this question we are given all the transition rates. So no use of this formula.

 

[johnpe21]

thansk a lot suraj for the explanation !