Let X[n] be a discrete-time Markov chain with states {1,2,3}, and the state transition probability matrix...

Transcribed Image Text:

Let X[n] be a discrete-time Markov chain with states {1,2,3}, and the state transition probability matrix [0.6 0.3 0.1] P = 0 1 0 0 (a) Assume X[0] = 1. Find the distribution of X[5]. (b) Assume X[0] =2. Find the distribution of X[5]. (c) Assume X[0] = 3. Find the distribution of X[5]. (d) Does X[n] have a steady-state distribution? Explain why. (e) Find the steady-state distribution if the state transition probability matrix is 0 1 0.6 0.3 0.1 0.1 0.9 0.3 0.7 (f) Find the steady-state distribution if the state transition probability matrix is P = 0 [0.2 0.1 0.7] 0 0.1 0.9 0 0.3 0.7 (g) How can you explain the results in parts (e) and (f)? What can you say about state 1? P = Let X[n] be a discrete-time Markov chain with states {1,2,3}, and the state transition probability matrix [0.6 0.3 0.1] P = 0 1 0 0 (a) Assume X[0] = 1. Find the distribution of X[5]. (b) Assume X[0] =2. Find the distribution of X[5]. (c) Assume X[0] = 3. Find the distribution of X[5]. (d) Does X[n] have a steady-state distribution? Explain why. (e) Find the steady-state distribution if the state transition probability matrix is 0 1 0.6 0.3 0.1 0.1 0.9 0.3 0.7 (f) Find the steady-state distribution if the state transition probability matrix is P = 0 [0.2 0.1 0.7] 0 0.1 0.9 0 0.3 0.7 (g) How can you explain the results in parts (e) and (f)? What can you say about state 1? P =