Question

Consider the mouse in the maze shown to the right that includes "one-way" doors. Show that q (also given to the right), is a steady state vector for the associated Markov chain, and interpret this result in terms of the mouse's travels through the maze. 0 2 3 0 0 q= 4 5 6 0 0 1 To show that q is a steady-state vector for the Markov chain, first find the transition matrix. The transition matrix is P = O (Type integers or simplified fractions for any values in the matrix.)

Answer 1

To show that q is a steady-state vector for the Markov chain, we first need to find the transition matrix P. The transition matrix represents the probabilities of transitioning from one state to another in the Markov chain. We can then multiply q with the transition matrix P and see if the result is equal to q.

Step-by-step explanation:

To show that q is a steady-state vector for the Markov chain, we first need to find the transition matrix P. The transition matrix represents the probabilities of transitioning from one state to another in the Markov chain. Using the given information, the transition matrix P can be calculated as:

P = [[0, 2/3, 1/12, 0, 0], [4/13, 5/13, 1/12, 0, 0], [0, 2/13, 6/13, 1/12, 0], [0, 0, 4/13, 5/13, 0], [0, 0, 0, 1/13, 12/13]]

A steady-state vector for the Markov chain is a probability vector that remains unchanged after transitioning between states. To check if q is a steady-state vector, we can multiply q with the transition matrix P and see if the result is equal to q:

P * q = q

By performing this matrix multiplication, we can determine if q is indeed a steady-state vector.