A (time-homogeneous) Markov chain built on states A and B is depicted in the diagram below....

A (time-homogeneous) Markov chain built on states A and B is depicted in the diagram below. What is the probability that a process beginning on A will be on B after 2 moves?

consider the Markov chain shown in Figure 11.14.

Figure 11.14- A state transition diagram.

Is this chain irreducible?
Is this chain aperiodic?
Find the stationary distribution for this chain.
Is the stationary distribution a limiting distribution for the chain?

Expert Solution

orchestra answered 1 year ago

Expected number of time intervals until the Markov Chain below is in state 2 again after...

Expected number of time intervals until the Markov Chain below is in state 2 again after starting in state 2? Matrix: [.4,.2,.4] [.6,0,.4] [.2,.5,.3]

Assume workers transition through the labor force independently with the transitions following a homogeneous Markov chain...

Assume workers transition through the labor force independently with the transitions following a homogeneous Markov chain with three states: • Employed full-time • Employed part-time • Unemployed The transition matrix is:   0.90 0.07 0.03 0.05 0.80 0.15 0.15 0.15 0.70  . • Worker Y is currently employed full-time • Worker Z is currently employed part-time Find the probability that either Y or Z, but not both will be unemployed after two transitions.

The following is the transition probability matrix of a Markov chain with states 1,2,3,4 ⎛⎞ .4...

The following is the transition probability matrix of a Markov chain with states 1,2,3,4 ⎛⎞ .4 .3 .2 .1 P=⎜.2 .2 .2 .4⎟ ⎝ .25 .25 .5 0 ⎠ .2 .1 .4 .3 (a) find the probability that state 3 is entered before state 4; If X0 = 1 (b) find the mean number of transitions until either state 3 or state 4 is entered.

Prove that for a Markov chain on a finite state space, no states are null recurrent.

Q4. Prove or disprove that τ is a stopping time (with respect to the Markov chain...

Q4. Prove or disprove that τ is a stopping time (with respect to the Markov chain {Xn|n ≥ 0} iff {τ > n} ∈ σ(X0, · · · , Xn), ∀ n ≥ 0 Q5. Prove or disprove that τ is a stopping time (with respect to the Markov chain {Xn|n ≥ 0}) iff {τ ≥ n} ∈ σ(X0, · · · , Xn), ∀ n ≥ 0 Q6. Let {Xn|n ≥ 0} be a Markov chain and A ⊂...

The following is the transition probability matrix of a Markov chain with states 1, 2, 3,...

The following is the transition probability matrix of a Markov chain with states 1, 2, 3, 4 P 0 1 2 3 0 .4 .3 .2 .1 1 .2 .2 .2 .4 2 .25 .25 .5 0 3 .2 .1 .4 .3 If Xnot = 1 (a) find the probability that state 3 is entered before state 4; (b) find the mean number of transitions until either state 3 or state 4 is entered.

For an irreducible Markov chain, either all states are positive recurrent or none are. Prove.

Let Xn be a Markov chain with states 0,1,...,9 and transition probabilities P0,0 = P0,1 =...

Let Xn be a Markov chain with states 0,1,...,9 and transition probabilities P0,0 = P0,1 = P9,8 = P9,9 = 1/2 an Pi,i = Pi,i+1 = Pi,i−1 = 1/3 for all 1 ≤ i ≤ 8. (a) Draw the transition diagram. (b) What is the probability that X1,X2,X3,X4 are all smaller than 3 given that X0 = 1? Hint: Create a simpler Markov chain with 4 states.

Let Xn be the Markov chain with states S = {1, 2, 3, 4} and transition...

Let Xn be the Markov chain with states S = {1, 2, 3, 4} and transition matrix. 1/3 2/3 0 0 2/3 0 1/3 0 1/3 1/3 0 1/3 0 1/3 2/3 0 a.) Let X0 = 3 and let T3 be the first time that the Markov chain returns 3, compute P(T3 = 2 given X0=3). Please show all work and all steps. b.) Find the stationary distribution π. Please show all work and all steps.

What are two markets depicted in the circular flow diagram? A. Individuals and households B. Replublicans...

What are two markets depicted in the circular flow diagram? A. Individuals and households B. Replublicans and Democrats C. Product and resources D. Market and command

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