申論題

4.Eigen value and matrix diagonization
Afinite state machine (FSM) has two states: state S1 and state S2. Let Prob(S₁ →S₂) denote the
probability that the machine moves from state S1 to state S2 in a cycle. Assume that the state
transition probabilities are fixed in every cycle: Prob(S₁→S₁)=0.3, Prob(S₁→＞S₂)-0.7,
Prob(S₂→S₁)=0.6, Prob(S₂→S₂)=0.4. Initially, the FSM is in state S1 at cycle 0.

(b) At the end of the second cycle, what is the probability that the FSM is in state S1? What is the probability that the FSM is in state S2?