A Markov chain with two states has transition matrix P . If the initial-state matrix is S 0 = 1 0 , discuss the relationship between the entries in the k th -state matrix and the entries in the k th power of P .
A Markov chain with two states has transition matrix P . If the initial-state matrix is S 0 = 1 0 , discuss the relationship between the entries in the k th -state matrix and the entries in the k th power of P .
Solution Summary: The author explains the relationship between the entries in the kth state matrix and the entry power of P in a Markov chain with two states.
A Markov chain with two states has transition matrix
P
. If the initial-state matrix is
S
0
=
1
0
, discuss the relationship between the entries in the
k
th
-state matrix and the entries in the
k
th
power of
P
.
A factory worker will quit with probability 1/2 during her first month, with probability 1/4 during her second month and with probability 1/8 after that. Whenever someone quits, their replacement will start at the beginning of the next month.
Model the status of each position as a Markov chain with 3 states. Identify the states and transition matrix.
Write down the system of equations determining the long-run proportions.
Suppose there are 900 workers in the factory. Find the average number of the workers who have been there for more than 2 months.
The transition matrix of a Markov Process is given by
7
9
10
10
T
1
3
10
10
V1
The steady state probability distribution vector for this Markov Process is denoted by v =
v2
Hence v1 + v2 =
Number
Making use of the above condition and solving a matrix equation, find the values of v1 and vɔ. Enter their exact values in the boxes below.
v1
v2 =
Suppose that a Markov chain with 4 states and with transition matrix P is in state 3
on the fifth observation. Which of the following expressions represents the probability
that it will be in state 4 on the tenth observation?
(A)
the (5, 10) entry of Pª
(B) the (3, 4) entry of Pš
(C)
the (10, 5) entry of Pª
(D) the (4, 3) entry of P3
(E)
the (5, 10) entry of P3
(F) the (4, 3) entry of P10
(G)
the (3, 4) entry of P10
(H) the (10, 5) entry of P3
Chapter 9 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
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