Question

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 1, determine average number of completed good, units.

Answer #1

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

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...

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.

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 ...

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.

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).

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

the Markov chain on S = {1, 2, 3} with transition matrix
p is
0 1 0
0 1/2 1/2;
1/2 0 1/2
We will compute the limiting behavior of pn(1,1) “by hand”.
(A) Find the three eigenvalues λ1, λ2, λ3 of p. Note: some are
complex.
(B) Deduce abstractly using linear algebra and part (A) that we
can write
pn(1, 1) = aλn1 + bλn2 + cλn3
for some constants a, b, c. Don’t find these constants yet.
(C)...

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...

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}

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