Markov Chain. Question 4 1[0. 23 0.45aIf P = |0.45 0.13 0.42 | is a transition matrix of a Markov chain,0. 66 0. 12 0. 22what is the value of a?0.24O 0.540.360.32O 0.41 Question 5Let Xn be a Markov chain with transition probability[0. 12 0.46 0.42P =0. 31 0. 26 0.43 |. Let the states be 1, 2, and 3. Find0. 11 0.73 0. 16P(X3 = 3|X1 =1, X2= 2).O 0.420.43) 0.110.73O 0.55

As per our guidelines we can solve first MCQ and rest can be reposted. Solution-: Q.4 Ans: We find…

Answered: Question 4 0. 23 0.45 a If P = | 0.45…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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What is the matrix form of the corresponding linear system of ODE?
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Markov Chain 0 10 0 0 0 0 0 1 0 0 0 0 0 0 1/2 0 1/2 0 0 0 0 0 0 0 1/4 0 1/2 1/4 0 0 0 P = 0 0 0 0 0 1/2 1/2 0 0 0 0 0 0 -0 0 2/3 1/3 0 0 0 0 0 0 1/2 1/2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 Find limp3n = (000100000) 0 0 00 where v oooooooo
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• General notation for Markov chains: P(A) is the probability of the event A when the Markov chain starts in state x, Pμ(A) the probability when the initial state is random with distribution μ. Ty = min{n ≥ 1: X₂ = y} is the first time after 0 that the chain visits state y. Px,y = Px(Ty < ∞) . Ny is the number of visits to state y after time 0. 4. Let Sn, n20 be a random walk on Z with step distribution 1-p 2 P 1) = 1/², P(X₁ = 1) = 2/₁ 2' 2' P(X₂ = 0) P(X₂ = − 1) = for some 0 < p < 1, p ‡ / . We may denote q=1 - p. That is, the increments (X₂)₁ are i.i.d. and S₂ = X₁ + … + Xn for n ≥ 1 and S = 0. Compute E[S2+1 Sn] for n ≥ 1. (b) Show that Mn = (q/p) Sn defines a martingale (with respect to (Xk)k-1). (c) Does the limit limn→∞ Mn exist almost surely? If yes, give a justification. If your answer is no, explain why. (d) Let T be the first time that S is equal to either −3 or 3. Compute P(ST = 3). Hint: You may use, without proof, the fact P(T<∞) = 1 and that the Optional Stopping Theorem…
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Question 4 0. 23 0.45 a If P = | 0.45 0.13 0.42 | is a transition matrix of a Markov chain, 0. 66 0.12 0.22 what is the value of a? 0.24 0.54 0.36 0.32 O 0.41