For this module you may want to look at the following TI-92 help modules.
Begin by entering the matrix A. You may want to consult the TI-92 help module Entering a Matrix Using the Data/Matrix Editor.
Because the matrix is so big, it is very easy to make an error. You should go over the entries carefully looking for mistakes. One nice easy check is to check that the entries in each column sum to one. This won't catch every possible error but it will catch some errors. The screens below define a function for checking the column sums and then verify that each column does sum to one.
Next enter the initial probability vector p0 as shown in the screen below.
The easiest way to proceed is to compute the vectors p1, p2, p3, p3, ... using matrix multiplication as shown in the screens below.
Notice what is happening. After each toss of the dice the probability of being in states 2 or 3 is a little higher -- that is, the longer the game goes on, the more likely a player is to have won or lost. Repeat the procedure above many more times until virtually everyone has won or lost. The screen below shows the result. Note that we changed the mode to display 4 digits to the right of the decimal point.
Notice that 46.91% of the time the player will win (state 2) and 53.09% of the time the player will lose (state 3).
If you were doing this problem without matrix multiplication you might enter the initial probability vector p0 as shown in the screen below.
and then use a little program to do the same computations as shown in the screens below.
