Question: (15 points) Consider a Markov chain with a state space S={1,2} and a one-step transition probability matrix: P:=[1/21/41/23/4] Answer the following questions: (Hint: recall the

(15 points) Consider a Markov chain with a state space S={1,2} and a one-step transition probability matrix: P:=[1/21/41/23/4] Answer the following questions: (Hint: recall the Markov property!) (a) (5 points) Compute P[X3=1X2=1,X1=1]= ? (b) (5 points) Compute P[X4=1X2=1,X1=1]= ? (c) (5 points) Suppose that the initially, the we have 5050 chance to be at state 1 or state 2 , that is, P[X0=1]=P[X0=2]=0.5. Compute P[X1=1]=

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