Question

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

Answer #1

urgent
Consider the Markov chain with state space {0, 1, 2, 3, 4} and
transition probability matrix (pij ) given 2 3 1 3 0 0 0 1
3 2 3 0 0 0 0 1 4 1 4 1 4 1 4 0 0 1 2 1 2 0 0 0 0 0 1 Find
all the closed communicating classes
Consider the Markov chain with state space {1, 2, 3} and
transition matrix ...

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...

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...

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}) =...

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).

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}

Let {??,?=0,1,2,…} be a Markov chain with the state space
?={0,1,2,3,…}. The transition probabilities are defined as follows:
?0,0=1, ??,?+1=? and ??,?−1=1−?, for ?≥1. In addition, suppose that
12<?<1. For an arbitrary state d such that ?∈?,?≠0, compute
?(??>0 ??? ??? ?≥1 |?0=?).

Consider a Markov chain {Xn; n = 0, 1, 2, . . . } on S = N = {0,
1, 2, . . . } with transition probabilities P(x, 0) = 1/2 , P(x, x
+ 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 =...

Let the markov chain consisting of states 0,1,2,3 have
the transition probability matrix
P = [0,0,1/2,1/2; 1,0,0,0; 0,1,0,0; 0,1,0,0]
Determine which state are recurrent and which are transient

Markov Chain
Transition Matrix for a three state system. 1 - Machine 1: 2-
Machine 2: 3- Inspection
1
2
3
1
0.05
0
.95
2
0
0.05
.95
3
.485
.485
.03
A. For a part starting at Machine 1, determine the
average number of visits this part has to each
state. (mean time until absorption, I believe)
B. 1-1, 2-2, & 3-3 represent BAD units (stays at state).
If a batch of 1000 units is started on Machine...

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