12. Diagonalization and Dynamical Systems

Markov Chains — Quiz

Test your understanding of markov chains with 5 practice questions.

Practice Questions

Question 1

What is the Markov property in a Markov chain?

Question 2

In the convention $x_{k+1}=Px_k$ with $x_k$ a column probability vector, what must each column of $P$ sum to?

Question 3

How many states does a Markov chain have if its transition matrix is a $3\times3$ matrix?

Question 4

Suppose $P=\begin{pmatrix}\frac23 & \frac14\\frac13 & \frac34\end{pmatrix}$ and $x_0=\begin{pmatrix}1\\0\end{pmatrix}$. What is $x_1=Px_0$?

Question 5

What is an absorbing state?