Wednesday, February 11, 2009

Transition Matrices (cont'd)

Well today in class, we spent most of our time reviewing the homework we had last night. And Mr. K just reviewed a little more about Transition Matrices, there was really nothing new for today.

Transition Matrices just shows you the probability of 2 or more things, if it would sell or if it will increase in days, weeks, or even years. Basically just probability of 2 or more things in the future.

I'll give you guys just another example of transtion matrices just in case some people are still not following. And hope this helps :).

Lets say you wanted to find out which air freshener would people use more in 10 years, Air Wick or Febreze.

First you would want to write the State Matrix, which means what is happening right now. So if the 20 people used Air Wick and 35 people used Febreze then the State Matrix would be as so. A for Air Wick and F for Febreze.

Here is the Transition Diagram, you can see how people change from one thing to another or if they just stay with that one product.

So, by looking at this diagram, 90% of the people that use Febreze stay with Febreze, but 10% change to Air Wick. And 70% of the people that use Air Wick stay with Air Wick, but 30% change to Febreze.

Now you have enough information to write a Transition Matrix. Here is how it will look like.

Now all you have to do is plug in the numbers, and follow the diagram above. And it will simply look like this.

And the only thing left to do is, multiply the State Matrix with the Transition Matrix. It will look like this.

You can punch this in your graphing calculator and put the State Matrix in matrix a, and the Transition Matrix in matrix b. Then just simply multiply matrix a and b, if you did it correctly you will get an answer like this.

Now you`ve got everything, you have to find out if Air Wick or Febreze was used more after 10 years. To do that, all you have to do is take your State Matrix (S) and your Transition Matrix (T) and just multiply to the power of 10. It will look like this.

So if you have punched in the matrix correctly you should have an answer like this.

If you are having trouble with transition matrices, you can also look at the nice example Alvina gave just under this post.

*Unit test coming up soon so hope you guys have been reading the posts everyday.

annnnnnnnd last but not least...

The next scribe is...


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