2. A Markov chain has the following transition matrix ||1/3 1/3 1/3|| P = 1/3 2/30 1/3 0 2/3 a. Draw a directed graph for the chain. b. Identify the communicating classes and classify them as periodic or aperiodic, transient or recurrent.

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A: F(x,y) : { (x+y)/42 ; x=1,2,3 y=1,2  ; 0 elsewhere } Mean : E(X) = sum(x*P(x))

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A: X1 ∼ N(0.7,1.4), X2 ∼ N(−0.5,1.2), X3 ∼ N(0.9,1.7), and X4 ∼ N(−0.2,2.1), independently.

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A: we have given a graph with edges and its points given as follows:

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A: We are given the deck as,Here, 4 - 1's4 - 2's4 - 3's4 - 4's5 - 4'sSo 20 cards in total

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A:

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