3. (35 points) Let X = {X: n=0,1,2,...} be a discrete time Markov chain on state...

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3. (35 points) Let X = {X: n=0,1,2,...} be a discrete time Markov chain on state space S = {2,4,6} with initial distribution (.2, .3, .5) and transition matrix (a) (5 points) Find Pr(X = 6). [.5.1.4] P=1.6 3 3 .5 .2 (b) (5 points) Find Pr(X = 4 | X = 6). (c) (5 points) Find Pr(X12 = 4 | X10 = 2). (d) (6 points) Find Pr(X3 = 6,X2=4|X0=2). 3. (35 points) Let X = {X: n=0,1,2,...} be a discrete time Markov chain on state space S = {2,4,6} with initial distribution (.2, .3, .5) and transition matrix (a) (5 points) Find Pr(X = 6). [.5.1.4] P=1.6 3 3 .5 .2 (b) (5 points) Find Pr(X = 4 | X = 6). (c) (5 points) Find Pr(X12 = 4 | X10 = 2). (d) (6 points) Find Pr(X3 = 6,X2=4|X0=2).