Thursday, February 12, 2009

Today in class, Mr.K put us into groups to go over our homework. Our homework was on Transition Matrices. We went over the homework and did some more review questions on Transitions Matrices.

Mr. K gave us an example of a Transition Matrix.

Example
Suppose that the population of a small island is classified into three distinct groups, children, teenagers and adults and that each year :

  • Children are born at a portion of 6% of the adult population , 1% of the children die


  • 10% of the children become teenagers , 5% of the teenagers die


  • 14% of the teenagers become adults , 7% of the adults die


This year, Youngville's population is 25 000. 5000 children, 18 000 teenagers and 2000 adults.



A) Write a row matrix that currently represents the population of Youngville.



The question is asking to right down the state matrix, a state matrix shows the information that that is currently given as a constant. Which is the population of Youngsville. We would label the matrix "S" which tells us that it is the state matrix.



A = Adults

T = Teenagers

C = Children




We would usually write the matrix in alphabetical order but in this case we would write it going oldest to youngest showing the population of the city more clearly.


B) Write a 3 x 3 transition matrix that shows how the population is changing over time.


To answer this question we would need to find out how the population changes.

The following matrix is labeled "T" which stands for "transition matrix."















Confusing? Well hopefully my explanation works. Adults can't turn back into teenagers so that's why there is a zero in the A,T position. 6% of the portion of adults become kids because adults make kids, and 1% of the children die, leaving 93% of the adults stay adults.


6% + 1% = 7%

100% - 7% = 93%


Teenagers can't go back into children so T,C becomes zero. 14% become adults, and 5% of the teenagers die, leaving 81% of the teenagers still teenagers.


14% + 5% = 19%

100% - 19% = 81%


Children can't just be adults right away so C,A becomes zero. 10% of the children become teenagers and 1% of the children die. Leaving 89% of the children stay children.


10% + 1% = 11%

100% - 11% = 89%


So that's how I understood the example Mr.K gave us. Hopefully this helped people understand it more.


IMPORTANT NOTE: Mr. K and the class decided that tomorrow will be another review class and that the pretest was moved to Tuesday as there is no school on Monday, Louis Riel day. The unit test will take place on the Friday of that week which is the 20th of February. Wednesday and Thursday we will be starting on our new unit.
The next scriber I choose is....
Mac

1 comments:

Lani said...

Hi Don,

Your scribe was very helpful! Yes, I was confused and your explanation was clear!

I liked the important note you added so that no one was mistaken about the test dates. You mentioned that Mr. K and the class decided; do you usually have input into the decisions on the test dates? Do other teachers offer that option too?

Best wishes,
Lani
Lani

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