Markov chain

[MethLover64]

first time posting, sorry for the inconvenience.

so let ,

We consider a Markov chain whose transition matrix is as follows:



Calculate the probability of event A to pass for n = 5, three times, through state 2.

with:
the three-time part is where I'm having difficulty, thank you for your time.

 

[Steven G]

There is no need to be sorry for posting a problem.
This is a help website where we help students to solve their problems but never solve problems for students. All this was in the posting guidelines which you should have read.

If you want help that is great but you will need to follow the posting guidelines by showing us what you have done so we know how you want to solve this problem and where you made any mistakes

 

[MethLover64]

Thank you for your reply,
English is my 4th language and I'm trying to be polite.

As for showing you my try in solving this exercise, with colleges closed, I'm attempting to learn on my own and I have not found a guide to solving these types of exercises the closest being trajectories.

so it doesn't have to be a solution but rather a hint?

 

[pka]

so let View attachment 24099 , We consider a Markov chain whose transition matrix is as follows:
View attachment 24100 Calculate the probability of event A to pass for n = 5, three times, through state 2.

with: View attachment 24101 the three-time part is where I'm having difficulty, thank you for your time.

Please explain the terms that are being used in this post. What is event A? "to pass for n=5? through state 2?
SEE HERE

 

[MethLover64]

I've typed the entirety of the exercise so the following are my understanding:
-event A could be anything and is not relevant in solving the problem. could indicate the change of state
-n : period of time could be in days, years..... ex(n = 0 is the start)
- translating the matrice to a graph :



thank you for replying