Question

The transition probability matrix of a Markov chain {Xn }, n = 1,2,3……. having 3 states...

The transition probability matrix of a Markov chain {Xn }, n = 1,2,3……. having 3
states 1, 2, 3 is P =
0.1 0.5 0.4
0.6 0.2 0.2
0.3 0.4 0.3
* and the initial distribution is P(0) = (0.7, 0.2,0.1)
Find:
i. P { X3 =2, X2 =3, X1 = 3, X0 = 2}
ii. P { X3 =3, X2 =1, X1 = 2, X0 = 1}
iii. P{X2 = 3}

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Xn is a Markov Chain with state-space E = {0, 1, 2}, and transition matrix 0.4...
Xn is a Markov Chain with state-space E = {0, 1, 2}, and transition matrix 0.4 0.2     ? P = 0.6 0.3    ? 0.5 0.3    ? And initial probability vector a = [0.2, 0.3, ?] a) What are the missing values (?) in the transition matrix an initial vector? b) P(X1 = 0) = c) P(X1 = 0|X0 = 2) = d) P(X22 = 1|X20 = 2) = e) E[X0] = For the Markov Chain with state-space, initial vector, and...
A Markov chain X0, X1, ... on states 0, 1, 2 has the transition probability matrix...
A Markov chain X0, X1, ... on states 0, 1, 2 has the transition probability matrix P = {0.1 0.2 0.7        0.9 0.1   0        0.1 0.8 0.1} and initial distribution p0 = Pr{X0 = 0} = 0.3, p1 = Pr{X0 = 1} = 0.4, and p2 = Pr{X0 = 2} = 0.3. Determine Pr{X0 = 0, X1 = 1, X2 = 2}. Please tell me what it means of the initial distribution why initial distribution p0 = Pr{X0...
Suppose that a production process changes states according to a Markov process whose one-step probability transition...
Suppose that a production process changes states according to a Markov process whose one-step probability transition matrix is given by 0 1 2 3 0 0.3 0.5 0 0.2 1 0.5 0.2 0.2 0.1 2 0.2 0.3 0.4 0.1 3 0.1 0.2 0.4 0.3 a. What is the probability that the process will be at state 2 after the 105th transition given that it is at state 0 after the 102 nd transition? b. What is the probability that the...
Let (pij ) be a stochastic matrix and {Xn|n ≥ 0} be an S-valued stochastic process...
Let (pij ) be a stochastic matrix and {Xn|n ≥ 0} be an S-valued stochastic process with finite dimensional distributions given by P(X0 = i0, X1 = i1, · · · , Xn = in) = P(X0 = i0)pi0i1 · · · pin−1in , n ≥ 0, i0, · · · , in ∈ S. Then {Xn|n ≥ 0} is a Markov chain with transition probability matrix (pij ). Let {Xn|n ≥ 0} be an S-valued Markov chain. Then the...
Given the probability transition matrix of a Markov chain X(n) with states 1, 2 and 3:...
Given the probability transition matrix of a Markov chain X(n) with states 1, 2 and 3: X = [{0.2,0.4,0.4}, {0.3,0.3,0.4}, {0.2,0.6,0.2}] find P(X(10)=2|X(9)=3).
1. Consider the Markov chain {Xn|n ≥ 0} associated with Gambler’s ruin with m = 3....
1. Consider the Markov chain {Xn|n ≥ 0} associated with Gambler’s ruin with m = 3. Find the probability of ruin given X0 = i ∈ {0, 1, 2, 3} 2 Let {Xn|n ≥ 0} be a simple random walk on an undirected graph (V, E) where V = {1, 2, 3, 4, 5, 6, 7} and E = {{1, 2}, {1, 3}, {1, 6}, {2, 4}, {4, 6}, {3, 5}, {5, 7}}. Let X0 ∼ µ0 where µ0({i}) =...
Consider the Markov chain with the state space {1,2,3} and transition matrix P= .2 .4 .4...
Consider the Markov chain with the state space {1,2,3} and transition matrix P= .2 .4 .4 .1 .5 .4 .6 .3 .1 What is the probability in the long run that the chain is in state 1? Solve this problem two different ways: 1) by raising the matrix to a higher power; and 2) by directly computing the invariant probability vector as a left eigenvector.
asasap Consider the Markov chain with state space {1, 2, 3} and transition matrix  ...
asasap Consider the Markov chain with state space {1, 2, 3} and transition matrix   1 2 1 4 1 4 0 1 0 1 4 0 3 4   Find the periodicity of the states. \ Let {Xn|n ≥ 0} be a finite state Markov chain. prove or disprove that all states are positive recurren
Consider a Markov chain with state space {1,2,3} and transition matrix. P= .4 .2 .4 .6...
Consider a Markov chain with state space {1,2,3} and transition matrix. P= .4 .2 .4 .6 0 .4 .2 .5 .3 What is the probability in the long run that the chain is in state 1? Solve this problem two different ways: 1) by raising the matrix to a higher power; and 2) by directly computing the invariant probability vector as a left eigenvector.
Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2,...
Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2, 3}, X0 = 0, and transition probability matrix (pij ) given by   2 3 1 3 0 0 1 3 2 3 0 0 0 1 4 1 4 1 2 0 0 1 2 1 2   Let τ0 = min{n ≥ 1 : Xn = 0} and B = {Xτ0 = 0}. Compute P(Xτ0+2 = 2|B). . Classify all...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT