A Markov chain has the transition matrix shown below: (Note: For questions 1, 2, and 4, express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal places).) ⠀ (1) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the second observation? 0.2 P = ⠀ 0.2 0.8] [0.4 0.6 (2) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the third observation? 0.384 ⠀ (3) If, on the first observation, the system is in state 2, what state is the system most likely to occupy on the third observation? (If there is more than one such state, which is the first one.) 0.36 ⠀ (4) If, on the first observation, the system is in state 2, what is the probability that it alternates between states 1 and 2 for the first four observations (.e., it occupies state 2, then state 1, then state 2, and finally state 1 again)? 0.64
A Markov chain has the transition matrix shown below: (Note: For questions 1, 2, and 4, express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal places).) ⠀ (1) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the second observation? 0.2 P = ⠀ 0.2 0.8] [0.4 0.6 (2) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the third observation? 0.384 ⠀ (3) If, on the first observation, the system is in state 2, what state is the system most likely to occupy on the third observation? (If there is more than one such state, which is the first one.) 0.36 ⠀ (4) If, on the first observation, the system is in state 2, what is the probability that it alternates between states 1 and 2 for the first four observations (.e., it occupies state 2, then state 1, then state 2, and finally state 1 again)? 0.64
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Pls ans all
![A Markov chain has the transition matrix shown below:
(Note: For questions 1, 2, and 4, express your answers as decimal fractions rounded to 4 decimal places (if they have
more than 4 decimal places).)
#
P =
S
(1) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the second
observation?
0.2
#
[0.2 0.81
[0.2
0.4 0.6]
5
(2) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the third observation?
0.384
(3) If, on the first observation, the system is in state 2, what state is the system most likely to occupy on the third
observation? (If there is more than one such state, which is the first one.)
0.36
(4) If, on the first observation, the system is in state 2, what is the probability that it alternates between states 1 and 2 for
the first four observations (i.e., it occupies state 2, then state 1, then state 2, and finally state 1 again)?
0.64](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88ceb3c4-679e-4b6b-b14f-62783ab2a438%2Fdc655462-c728-4d96-852e-c9b05e274134%2Fd359y5c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A Markov chain has the transition matrix shown below:
(Note: For questions 1, 2, and 4, express your answers as decimal fractions rounded to 4 decimal places (if they have
more than 4 decimal places).)
#
P =
S
(1) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the second
observation?
0.2
#
[0.2 0.81
[0.2
0.4 0.6]
5
(2) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the third observation?
0.384
(3) If, on the first observation, the system is in state 2, what state is the system most likely to occupy on the third
observation? (If there is more than one such state, which is the first one.)
0.36
(4) If, on the first observation, the system is in state 2, what is the probability that it alternates between states 1 and 2 for
the first four observations (i.e., it occupies state 2, then state 1, then state 2, and finally state 1 again)?
0.64
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