A BThe transition matrix for a Markov chain is shown to the right04 06P=B0.5 0.5(A) If S, =01find Sz. S4, S. Can you identity a state matrix S that the matrices S, seem to be approaching?(B) Repeat part (A) for S, -10](C) Repeat part (A) for Sy = 0.2 0.8(D) Find SP for any matrix S you identified in parts (AC).(E) Desoribe the long-term behavior of the state matrices of this Markov chain.(A) If initial state matrix Sy01find the state matrices S. S. S

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Answered: A B The transition matrx for a Markov…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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4. Find the stationary distribution of the Markov chain shown below using the reversible property. OFE 1/2 I 2 1/2 1/4 5/12 3 1/3 1/6 7/12 4 1/4 1/8 7/8 5
Suppose that a Markov chain has the following transition matrix a, az az as a s 3 000 The recurrent states are a 4 4 a₂000 P=a₂00 0 0 a003 as 1 0 0 0
PREVIOUS ANSWERS ASK YOUR TEACHER Let P = 0.5 0.1 0.5 0.9 0.5 be the transition matrix for a Markov chain with two states. Let x0 = = be the initial state vector 0.5 for the population. What proportion of the state 2 population will be in state 2 after two steps?
[ 0.2 0.4 0.4 P(YIX) = |0.25 0.5 0.25| 0.4 0.3 0.3. 3- Draw the markov state diagram for the channel transition matrix shown beside.
• 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…
If she made the last free throw, then her probability of making the next one is 0.7. On the other hand, If she missed the last free throw, then her probability of making the next one is 0.2. Assume that state 1 is Makes the Free Throw and that state 2 is Misses the Free Throw. (1) Find the transition matrix for this Markov process. %3D
A Markov system with two states satisfies the following rule. If you are in state 1 then of the time you change to state 2. If you are in state 2 then of the time you remain in state 2. state 1 Write the transition matrix for this system using the state vector v state 2 T = Find the long term probability (stable state vector). vs
3. [0/1 Points] MY NOTES Let P = DETAILS Need Help? PREVIOUS ANSWERS ASK YOUR TEACHER PRACTICE ANOTHER POOLELINALG4 3.7.003. be the transition matrix for a Markov chain with two states. Let x for the population. What proportion of the state 2 population will be in state 2 after two steps? 86% Read It Watch It 0.5 0.5 be the initial state vector.
E5.2. Consider a Markov chain with state space S = {1,2,3, 4, 5, 6} and transition matrix 1 0 0 0 0 0 0 0 0 P = 0 0 0 1 0 0 0 0 0 0 0 1 0 (a) Draw the transition graph of this chain. (b) Show that state 1 is absorbing and conclude that it is positive re- current. (c) Show that states 2 and 3 are transient. (d) Verify that states 4, 5 and 6 are positive recurrent.
c) Consider the transition Markov chain with three states S = (1, 2, 3) as shown below. %3D 1 Given that; P(X, = 1) = 3' fine P(X, = 1,X, = 2,X2 = 3) N/3 1/2 1/2 1/4 1/2 1/4
A Markov system with two states satisfies the following rule. If you are in state 1 then of the time you change to state 2. If you are in state 2 then of the time you remain in state 2. At time t = 0, there are 100 people in state 1 and no people in the other state. state 1 Write the transition matrix for this system using the state vector v = state 2 T = Write the state vector for time t = 0. Vo Compute the state vectors for time t = 1 and t = 2. Vị = V2

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A B The transition matrx for a Markov chain is shown to the right 0.4 06 P= 0.5 05 (A) H S=01nd S. S. S Can you identity a state matrix Sthat the matices S, seem to be approaching? (8) Repeat part (A) for S 10 (C) Repeat part (A for S 02 0.8