Consider a Markov Chain with three possible states S = {1,2,3}, that has the following transition matrix. [1/2 1/4 1/4] P = |1/3 [1/2 1/2 2/3 (a) Draw the state transition diagram for this chain. (b) P( X5 = 2 | X4, = 1) (c) P(X3 = 2| X2 = 2) (d) If we know P(Xo = 1) = 1/4, find P(Xo = 1,X1 = 2) (e) If we know P(X, = 1) = 1/4, find P(X, = 1,X, = 2,X2 = 3)

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Assignment-l
Consider a Markov Chain with three possible states S = {1,2, 3}, that has the following
transition matrix.
[1/2 1/4 1/41
P = |1/3
[1/2 1/2
2/3
(a) Draw the state transition diagram for this chain.
(b) P( X5 = 2 | X4 = 1)
(c) P( X3 = 2| X2 = 2)
(d) If we know P(X, = 1) = 1/4, find P(X, = 1,X1 = 2)
(e) If we know P(X, = 1) = 1/4, find P(X, = 1,X, = 2, X, = 3)
%3D
%3D
Transcribed Image Text:Assignment-l Consider a Markov Chain with three possible states S = {1,2, 3}, that has the following transition matrix. [1/2 1/4 1/41 P = |1/3 [1/2 1/2 2/3 (a) Draw the state transition diagram for this chain. (b) P( X5 = 2 | X4 = 1) (c) P( X3 = 2| X2 = 2) (d) If we know P(X, = 1) = 1/4, find P(X, = 1,X1 = 2) (e) If we know P(X, = 1) = 1/4, find P(X, = 1,X, = 2, X, = 3) %3D %3D
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