My Math Forum Markov Chain (transition matrix)

March 12th, 2009, 12:35 AM   #1
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Markov Chain (transition matrix)

Hey can anyone please help me obtain the transition of the markov chain with states being the number of projects the architect has in hand at the beginning of a month.

Quote:
 An architect can handle up to 3 projects at once. During any month there is a probability of 0.5 of acquiring one new project (to start the next month) provided the architect knows that the project can be handled, otherwise no new projects are acquired. That is, the architect decides to take the honourable course of not taking on a new project for the next month unless it is known that it can be handled. Existing projects are equally-likely to finish by the start of the next month or to continue, independently of each other.
Thank you.

 March 12th, 2009, 07:51 AM #2 Senior Member   Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0 Re: Markov Chain (transition matrix) Try writing everything in terms of what can happen, with what probabilities. For instance, if $X_n=i$ and $X_{n+1}=j,$ then: $i=0,\ j=0\ \Rightarrow$ no new projects are acquired, prob. 0.5. $i=0,\ j=1\ \Rightarrow$ a new project is acquired, prob. 0.5 $i=0,\ j>1\ \Rightarrow=$ not possible - only one project can be acquired in any month, prob. 0 $i=1,\ j=0\ \Rightarrow$ a project is finished and no new projects are acquired, prob. 0.5 x 0.5 $i=1,\ j=1\ \Rightarrow$ ? $i=1,\ j=2\ \Rightarrow$ ? etc. Remember that $\sum_{j\in S} p_{ij}=1$ for any $i\in S$ where $S$ is the state space.
 March 12th, 2009, 02:18 PM #3 Newbie   Joined: Mar 2009 Posts: 2 Thanks: 0 Re: Markov Chain (transition matrix) Thank you very much for your reply. And I can see what you're trying to say, I understand it now, thanks again. Last edited by skipjack; January 21st, 2016 at 09:26 PM.
 January 21st, 2016, 08:31 PM #4 Newbie   Joined: Jan 2016 From: Ethiopia Posts: 1 Thanks: 0 Math Focus: DouglasmiXM This seems like an awesome place! Cheers, Stumbled upon this space and just checking out what mymathforum.com is all about!

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