Matrices

Today's class was just basically a recap of last nights homework. The homework was confusing to a lot of us so here is one of the questions. I will try to see if i can give you a better understanding of this question based on what i learned.

1. If a train is late on one day, there is a 90% probability that the same train will be on time the next day, while if the train is on time, there is a 20% chance it will be late the next day. If in a given week it arrives on time on Monday, compute the probabilities that it will be on time or late for each of the subsequent days of the week. What would the corresponding probabilities have

been if the train had been late on Monday.

In this matricx (T) represents on time and (L) represents late. So as you can see the numbers stated in the problem have been inserted into matricx. Now because there is a .20 there has to be a .80 at the (T) (T) location. This is because each row must equal 100 or 1 depending if u are using whole numbers or percents. So following this rule there has to be a .10 at the (L) (L) location.

Now that we got the transition matricx we need what is called a state matricx. A state matricx is what happens first, because the train was on time on Monday the state matricx has to be;The (1) represents the on time colum and the (0) reprsents the late colum.

So to find the percentages of the train coming late or on time you would take the transition matricx and multiply it by the state martricx like this;

If u muiltpy these two matrices you will get the percents of the train being late or on time for the next day. If you multiply the result by the transition matricx you will get the percents for the third day and so on and so on ........

Now if the train happened to be late on that first Monday then the transition matricx would stay the same and the only difference with the state matricx is that the 1 and the 0 would be switched around.


Definitions:

Transition Matricx.....is the matricx showing how things change over time.

State Matricx.....is the matricx in which things begin

Another thing to remember is that if you are trying to find what the numbers stabilize at, rather then keep pressing enter on your calculator just rise the transition matricx to a high number and you will be able to see the numbers at which the amount stabilized. But remember this way only works if you are not interested in finding the exact time that the number stabilized.

I hope my scribe made it easier for you guys to understand things.

The next scribe is chris