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

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 ...

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).

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...

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 =...

You are given a transition matrix P. Find the
steady-state distribution vector. HINT [See Example 4.]
A) P =
5/6
1/6
7/9
2/9
B) P =
1/5
4/5
0
5/8
3/8
0
4/7
0
3/7

Consider a batch manufacturing process in which a machine
processes jobs in batches of three units. The process starts only
when there are three or more jobs in the buffer in front of the
machine. Otherwise, the machine stays idle until the batch is
completed. Assume that job interarrival times are uniformly
distributed between 2 and 8 hours, and batch service times are
uniformly distributed between 5 and 15 hours.
Assuming the system is initially empty, simulate the system
manually...

(1) In a 2 state system, an unreliable machine has a 10% chance
of breaking down and a 60% chance of being repaired. At a steady
state, what is the probability that the machine is down? Enter your
answer as a percentage (XX.X)
(2) For the system described in problem (1) above, what is the
probability that the machine is up?Continue to assume that the
system is at a steady-state. Enter your answer as a percentage
(XX.X)
3) What is...

please post solutions using R
Consider a batch manufacturing process in which a machine
processes jobs in batches of three units. The process starts only
when there are three or more jobs in the buffer in front of the
machine. Otherwise, the machine stays idle until the batch is
completed. Assume that job interarrival times are uniformly
distributed between 2 and 8 hours, and batch service times are
uniformly distributed between 5 and 15 hours.
Assuming the system is initially...

Problem 1.18
Values for some properties of the n = 1 state of the Bohr
model of the hydrogen atom are given in the following table. Write
the value of the same parameter (in the same units) for the
n = 2 state.
parameter
n = 1
n = 2
momentum (kgms)
1.99 ⋅ 10-24
de Broglie wavelength (nm)
0.333
kinetic energy (Eh)
0.500
transition energy to n = 3 (Eh)
0.444
Part A
Determine the momentum for the n...

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