The state vector for stage j of a Markov chain with n states:
A)is a 1 x n matrix.
B)contains transition probabilities for stage j.
C)contains only nonzero values.
D)contains the steady-state probabilities.

Question

Quizplus · Accepted Answer

The state vector for stage j of a Markov chain with n states is a row vector containing the probabilities of being in each state at stage j. Therefore, it has dimensions 1 x n, making choice A the correct option.

B is incorrect because transition probabilities would be contained in the transition probability matrix, not the state vector.

C is incorrect because the state vector can contain zero probabilities, indicating that a particular state is not currently occupied.

D is incorrect because the steady-state probabilities would be found by taking the limit of the state vector as the number of stages approaches infinity, not by looking at a specific stage j.

The State Vector for Stage J of a Markov Chain