Question

How do you find the steady state vector of a Markov Chain?

A) By multiplying the transition matrix by itself repeatedly
B) By solving a system of linear equations involving the transition matrix
C) By taking the determinant of the transition matrix
D) By finding the eigenvalues of the transition matrix

Answer 1

To find the steady state vector of a Markov Chain, solve a system of linear equations that involves the transition matrix, ensuring the sum of the vector elements equals 1.

Step-by-step explanation:

To find the steady state vector of a Markov Chain, you should choose option B) By solving a system of linear equations involving the transition matrix. A steady state vector, also known as a stationary distribution, is a vector that remains unchanged after applying the transition matrix, which means that when you multiply the transition matrix by the steady state vector, you get the steady state vector it self.

Here's a step-by-step approach to finding it:

1. Identify the transition matrix of the Markov Chain.
2. Set up a system of equations by equating the product of the transition matrix and the steady state vector to the steady state vector itself.
3. Include the condition that the sum of the probabilities in the steady state vector must equal 1.
4. Solve the system of linear equations to find the values of the steady state vector.

It is not sufficient to multiply the transition matrix by itself repeatedly (option A), nor is it correct to take the determinant of the transition matrix (option C) or find the eigenvalues (option D) to directly obtain the steady state vector.