Is $S_0 = (1,0)^T$ the only possible initial state for this Markov chain?

Conditions

• The system is a Markov chain with states A and B.
• The entries of the initial state vector are probabilities.
• The sum of the probabilities in the initial state vector must equal 1.

Reasoning, step by step

1. Recognize that the transition diagram defines the rules for moving between states.
2. Understand that the initial state vector $S_0$ defines where the system starts.
3. Note that the speaker explicitly states the choice of $S_0 = (1,0)^T$ is asserted for the example.
4. Conclude that any vector with non-negative entries summing to 1 is a valid initial state.

Example

The speaker says the fact that it says 1 and 0 means there is a 100% probability it starts in state A and a 0% probability it starts in state B, and adds, "I've just asserted this."

Common misconceptions

• Confusing the initial state with something forced by the transition probabilities.
• Believing that a Markov chain must always start in a specific state defined by its transition matrix.

Watch the explanation

Explore next

• What does $S_1$ mean in a Markov chain example?
• Why introduce a matrix instead of just reading the transition diagram?