Which state does each component of $S_0$ correspond to?

Conditions

• The system is represented by a state vector.
• The ordering of states is fixed.

Reasoning, step by step

1. Identify the state vector $S_0$.
2. Look at the top component and associate it with the first state, A.
3. Look at the bottom component and associate it with the second state, B.
4. Generalize that each state gets one component in the vector.

Example

The speaker says the top component refers to state A and the bottom component to state B, and adds that if there were more components such as A, B, C, then the vector would have three components.

Common misconceptions

• Assuming the order of components is arbitrary or can be changed without updating the transition matrix.
• Thinking a Markov-chain state vector is limited to two components regardless of the number of states.

Watch the explanation

Explore next

• Is $S_0 = (1,0)^T$ the only possible initial state for this Markov chain?
• In this video, what do the rows and columns of the transition matrix represent?