Tuesday, February 10, 2009

Transition Matrices

Today's class we started off with reviewing yesterdays homework before we moved on to 'Transition Matrices'
From what I understand, a Transition Matrices is a matrix that shows things that change in time.
Your trying to find the probability of things that you want to know in the future.
When doing a transition matrix you would have to find the state matrix ( which tells you the current state of affairs) 
and the transition matrix ( which tells you what's going to change). 

When writing a 'State matrix' you would have to know the current event that is taking place to fill in the matrices.
For example the state matrix would look like this,
S = [ number of blue shoes number of red shoes]

If the person had 10 blue shoes and 2 red shoes then your state matrix would be..
S = [ 10 2 ]

If you wanted to find out if a person wanted to use blue shoes, they have a 90% chance that they would use red shoes.
If the person wanted to wear red shoes, they would have a 50% chance that they would wear blue shoes.

To figure this out, you can also use a 'transition diagram' to help you 
through the process.
This way you can also see what the changes are.
So your transition diagram would look like the picture below.

 From here you can see what you need to make a 'Transition matrix' .

Then you would have to plug in the numbers. 

You transition matrix would equal to..

T = [ 6      9.2]

And that's how I believe you do a transition matrix.

The nest scriber I choose is ...
KYLE!! :)


Daniel said...

I think the probabilities have to add up to 100% for this exercise, by having them add up to more than 100%, you suggest that the shoppers will begin buying two or three brands... I believe.

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