a) Find P(X1 P(X21 = 1|X19 = 2). = 2|Xo = 0), P(X4 1|X3 = 0, X2 = 1), P(X2 = 1|Xo = 1) and %3D %3D %3D %3D %3D %3D %3D %3D %3D
a) Find P(X1 P(X21 = 1|X19 = 2). = 2|Xo = 0), P(X4 1|X3 = 0, X2 = 1), P(X2 = 1|Xo = 1) and %3D %3D %3D %3D %3D %3D %3D %3D %3D
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Mm4
![Consider the situation in Exercise 2, point b). Does the steady state probabilities solve the following
set of equations?
0.7T0 +0.371+0.172 = T0
0.2то + 0.5л]+0.4тэ — T1
| To + T1+ 72 =1
no
yes
Exercise 2:
Using certain criteria the stock marked has what could be called a bad day (state 0), an
average day (state 1) or a good day (state 2). Let X, be the state on day n. The process
{X,: n = 0, 1, 2, 3, . } is assumed to be a Markov chain with the following transition
matrix,
Y 0.7 0.2 0.1
P =
0.3 0.5 0.2
0.1 0.4 0.5
and with
0.56 0.28 0.16)
p²
0.38 0.39 0.23
0.24 0.42 0.34
a) Find P(X1
2|Xo
0), P(X4
1|X3
0, X2 =
1), P(X2 = 1|X, = 1) and
%3D
%3D
%3D
%3D
%3D
P(X21 = 1|X19 = 2).
(Wait with point b) below until you have learned about steady state probabilities)
b) Find the steady state (equilibrium) equations for this system and solve them.
If the system starts in Xo = 0, what is the probability that P(X,= 0|Xo = 0) when
n becomes large?
%3D
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffafa7ad-5c0a-41f9-b550-d1e2021fb7de%2F0f5ea48b-e7ec-4d2f-b880-2dc007825f65%2Fli6rtro_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the situation in Exercise 2, point b). Does the steady state probabilities solve the following
set of equations?
0.7T0 +0.371+0.172 = T0
0.2то + 0.5л]+0.4тэ — T1
| To + T1+ 72 =1
no
yes
Exercise 2:
Using certain criteria the stock marked has what could be called a bad day (state 0), an
average day (state 1) or a good day (state 2). Let X, be the state on day n. The process
{X,: n = 0, 1, 2, 3, . } is assumed to be a Markov chain with the following transition
matrix,
Y 0.7 0.2 0.1
P =
0.3 0.5 0.2
0.1 0.4 0.5
and with
0.56 0.28 0.16)
p²
0.38 0.39 0.23
0.24 0.42 0.34
a) Find P(X1
2|Xo
0), P(X4
1|X3
0, X2 =
1), P(X2 = 1|X, = 1) and
%3D
%3D
%3D
%3D
%3D
P(X21 = 1|X19 = 2).
(Wait with point b) below until you have learned about steady state probabilities)
b) Find the steady state (equilibrium) equations for this system and solve them.
If the system starts in Xo = 0, what is the probability that P(X,= 0|Xo = 0) when
n becomes large?
%3D
%3D
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