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The transition matrix $P$ is constructed such that the entry in row $i$ and column $j$ represents the probability of moving from state $i$ to state $j$. Each row must sum to 1.

Conditions: The Markov chain has a finite number of states.; The state diagram shows all possible transitions and their probabilities.

The transition matrix $P$ is constructed such that the entry in row $i$ and column $j$ represents the probability of moving from state $i$ to state $j$. Each row must sum to 1.

Conditions: The Markov chain has a finite number of states.; The state diagram shows all possible transitions and their probabilities.