(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.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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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.
Transcribed Image 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.
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