Tips on how I would find the transition matrix for the following phenomenon?

Question

how would I go about finding the transition matrix for the following phenomenon (which can be modeled as a Markov process)?

Any hints or advice is appreciated!

During a study break, a student's evening habits vary from day to day:

• If he studies one night, there is a 20% probability that he will not study the following night.
• There is a 10% probability that he will not study for two nights in succession.

Answer 1

If we have 2 states: S = Study, S' = No Study.

Then we can form a 2 X 2 matrix(pardon my drawing, I am new at this)

 S S'

S .8 .2

S' .9 .1

So the first row answers itself from your question. The row S says our current state(night 1) the student is studying. The column S says our next state(night 2) the student has an 80% chance of studying. So column S'(night 2) must be 20% he won't study.

In the second part of your question we know if he does not study in the current state(night 1) that there is a 10% chance he does not study next state( night 2).

The rows must sum to 1(probability must add up to 1). So there is a 90% if the student does not study in the current state(night 1), he will study in the next state(night 2)