What does a transition diagram represent in a Markov chain?

Conditions

• The diagram is being used for a Markov chain.
• Each arrow label is interpreted as a one-step transition probability.

Reasoning, step by step

1. Identify the nodes, which represent the possible states of the system.
2. Identify the directed arrows, which represent the allowed transitions between states.
3. Read the numerical labels on the arrows, which describe the probability of moving from the source state to the target state in one iteration.

Example

In the displayed example, the states are A and B. The diagram shows a self-loop on A labeled 0.75, an arrow from A to B labeled 0.25, an arrow from B to A labeled 0.4, and a self-loop on B labeled 0.6.

Common misconceptions

• Thinking that the arrows represent the actual path the system will take, rather than the probabilities of all possible paths.
• Assuming that the numbers on the arrows represent the total probability of being in a state, rather than the transition probability between two states.

Watch the explanation

Explore next

• What does the 0.75 label on the arrow from A to A mean?
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