Question

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

The​ (i,j)-entry in a transition matrix P gives the probability of a move from state j to state i.

Choose the correct answer below.

A. The statement is true because this is the definition of the transition matrix.

B. The statement is false because the​ (i,j)-entry in a transition matrix gives the probability of being in state i after j steps.

C. The statement is false because the​ (i,j)-entry in a transition matrix gives the probability of being in state j after i steps.

D. The statement is false because the​ (i,j)-entry in a transition matrix gives the probability of a move from state i to state j.

Answer 1

The statement in question is false because the (i,j)-entry in a transition matrix gives the probability of moving from state j to state i, not the other way around.

Step-by-step explanation:

The statement in question is false because the (i,j)-entry in a transition matrix gives the probability of moving from state j to state i, not the other way around. In other words, it represents the probability of transitioning from state j to state i, not the probability of being in state i after j steps or being in state j after i steps.