Question
(a) State the condition for the stationary distribution of an irreducible Markov chain to exist and...
(a) State the condition for the stationary distribution of an irreducible Markov chain to exist and be unique.
(b) What is the additional condition required for the limiting distribution to also exist and be equal to the unique stationary distribution for an irreducible Markov chain? Explain why it is needed.
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(a) State the condition for the stationary distribution of an irreducible Markov chain to exist and...
(a) State the condition for the stationary distribution of an
irreducible Markov chain to exist and be unique.
(b) What is the additional condition required for the limiting
distribution to also exist and be equal to the unique stationary
distribution for an irreducible Markov chain? Explain why it is
needed.
Consider a Markov chain on {0,1,2, ...} such that from state i, the chain goes to...
Consider a Markov chain on {0,1,2, ...} such that from state i, the chain goes to i + 1 with probability p, 0 <p <1, and goes to state 0 with probability 1 - p.
a) Show that this string is irreducible. b) Calculate P0 (T0 = n), n ≥ 1. c) Show that the chain is recurring.
Consider a Markov chain {Xn; n = 0, 1, 2, . . . } on S...
Consider a Markov chain {Xn; n = 0, 1, 2, . . . } on S = N = {0,
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+ 1) = 1/2 ∀x ∈ S, .
(a) Show that the chain is irreducible.
(b) Find P0(T0 = n) for each n = 1, 2, . . . .
(c) Use part (b) to show that state 0 is recurrent; i.e., ρ00 =...
Initial state and limit state In the class I have shown you with the population example...
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In the class I have shown you with the population example of
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This corresponds to the case of p(0) = [0.5, 0.5] and limiting
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The state of a process changes daily according to a two-state Markov chain. If the process...
The state of a process changes daily according to a two-state
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Every day a message is sent. If the state of the Markov chain
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Markov Chain Matrix 0 1 0 0.4 0.6 1 0.7 0.3 a.) suppose process begins at...
Markov Chain
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0 1
0 0.4 0.6
1 0.7 0.3
a.) suppose process begins at state 1 and time =1 what is the
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b.) What is the steady state distribution of the Markov Chain
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what is the throughput of non-persisten csma. by using a two-state markov chain. when nodes are...
what is the throughput of non-persisten csma. by using a
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Make sure is two-state not three-state. thank
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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...
Suppose that a production process changes states according to a Markov process whose one-step probability transition...
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0 1 2 3
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1 0.5 0.2 0.2 0.1
2 0.2 0.3 0.4 0.1
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Is the confidence interval appropriate? • Independence Condition: Required. Guaranteed if the sample was random. If...
Is the confidence interval appropriate?
• Independence Condition: Required. Guaranteed if the sample was
random. If not, we have to consider whether it there’s any reason
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• <...
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