Markov Chain Matrix

Question

Can any make Markov chain matrix of this problem? We can model the educational journey of a student using a Markov chain. In our model there are 4 states, representing whether a student is registered in year 1, year 2, has taken their exam or has dropped out. They report that of the first year students, 80% continue to year 2, and the rest drops out. Of the year 2 students, 20% re-register in year 2, 60% take their degree and 20% drop out. The states of having dropped out or taken ones degree can be seen as absorbing states. i also have some question about it. (a) Write down the transition matrix for this model. Explain how you have numbered the states. (b) Are there any assumptions in the model that strike you as dubious? To evaluate the educational quality, we are interested in some statistics. (c) What proportion of students that start the programme will drop out? (On average.) (d) What proportion of students will take their degree? (e) How many years will a student spend on average at the college before dropping out or taking their exam? please Explain the answer.

Answer 1

The transition matrix is

$A = \begin{bmatrix} 0 & .80 & 0 & .20 \\ 0 & .20 & .60 & .20 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$

Where the entry $A_{ij}$ is the probability that we go to state $j$ from state $i$. The states are as follows:

1. Year One
2. Year Two
3. Degree
4. Drop Out