In this simple model, we have only two states (D and E). The probability distribution of states at time 7 depends only on the state at time 6. Time 1 2 3 4 5 6 7 State . . . . . D ? A Simple Markov Model (continued) The conditional distribution of states at time 7, given the state at time 6 is the same as the conditional distribution of states at time 7, given the complete sequence of previous states. The conditional distribution is usually given by a transition probability matrix. Time 7 State

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... Time 6 State D E D P(D|D) P(E|D) E P(D|E) P(E|E) A Simple Markov Model (continued) In this simple example, we have focused on times 6 and 7. More generally, we could have discussed times t-1 and t. The transition probability matrix is often the same for all t, but that is not necessarily the case and will not be the case in our application. Time t State Time t-1 State D E D P t (D|D) P t (E|D) E P t (D|E) P t (E|E)