The transition matrix P for a three-state Markov chain with state space S= {1,2,3} is [0.3 P = 0.6 0.1 0.3 0.4 0.6] а b Thus, P32 = 0.4, P13 = b. (a) Calculate the matrix P(2) (in terms of the...

Extracted text: The transition matrix P for a three-state Markov chain with state space S= {1,2,3} is [0.3 P = 0.6 0.1 0.3 0.4 0.6] а b Thus, P32 = 0.4, P13 = b. (a) Calculate the matrix P(2) (in terms of the constants a and b). (b) If the probability of the system being in state 3 at step n+ 2 if it is in state 1 at step n is 0.48, find the values of a and b. Express each of your calculations in exact decimal form.