Question

Determine whether the statement below is true or false. Justify the answer.

The rows of a transition matrix for a Markov chain must sum to

A. The statement is true because each row must be a probability vector.
B. The statement is false because each column must be a probability vector.
C. The statement is false because sum can be any number in the interval [0,1]
D. The statement is false because the requirement is that the sum of each column must be in the interval [0,1]

Answer 1

A transition matrix of a Markov chain is true because each row, representing state transition probabilities, must sum to one to be considered a probability vector.

Step-by-step explanation:

The statement regarding the transition matrix for a Markov chain is true because each row must sum to one. Each row in a transition matrix represents the probabilities of transitioning from one state to the other states in the next step of the chain. Because these are probabilities, the sum of the probabilities in a single row must equal 1, which ensures that the total probability of transitioning from a given state to any of the possible states is certain. This is analogous to a probability vector, where each element represents the probability of a particular event, and all events are mutually exclusive and collectively exhaustive.