Explanation Given Information: The stable distributions for the provided stochastic matrix [ .4 0 .9 0 1 0 .6 0 .1 ] are [ .6 0 .4 ] and [ 0.3 0.5 0.2 ] respectively. Formula used: The stable distribution for the matrix X = [ ] , could be determined by solving the system of linear equations as, 1. The sum of entries of X = 1 . 2. And A X = X . Proof: Consider the stable distributions, [ .6 0 .4 ] and [ 0.3 0.5 0.2 ] for the provided stochastic matrix, [ .4 0 .9 0 1 0 .6 0 .1 ] . Consider the stable distribution [ .6 0 .4 ] and [ 0.3 0.5 0.2 ] Here, the sum of entries of X is 1. 0.6 + 0 + 0.4 = 1 Similarly, 0.3 + 0.5 + 0.2 = 1 So, first condition is satisfied. From the formula for the stable distribution of the matrix X = [ ] , determined by solving the system of linear equations as, A X = X Thus, [ .4 0 .9 0 1 0 .6 0 .1 ] [ .6 0 .4 ] = [ .6 0 .4 ] and [ .4 0 .9 0 1 0 .6 0 .1 ] [ 0.3 0.5 0.2 ] = [ 0.3 0.5 0.2 ] So, these two matrices [ .6 0 .4 ] and [ 0.3 0.5 0.2 ] are stable distribution. When given arbitrary initial distribution for the value of 0 of the stochastic matrix, [ ] 0 ≠ [ 0.6 0 0.4 ] or [ 0.3 0.5 0.2 ] . Let take the initial distribution [ ] 0 = [ 0.5 0.3 0.2 ] . Now, calculate the matrix A 10 . First calculate the matrix A 2 ; A 2 = A ⋅ A = [ .4 0 .9 0 1 0 .6 0 .1 ] [ .4 0 .9 0 1 0 .6 0 .1 ] = [ 0.7 0 0.45 0 1 0 0.3 0 0.55 ] Calculate the matrix A 3 ; A 3 = A ⋅ A 2 = [

12th Edition

ISBN: 9780134464053

Author: HAIR

Publisher: YUZU

See similar textbooks

Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could co…

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a…

Videos

Question

Chapter 8.2, Problem 25E

To determine

To prove: The matrix [0.600.4] and [0.30.50.2] are both stable distributions for the stochastic matrix

[.40.9010.60.1]. Also, explain the reason due to which this fact does not contradict the uniqueness of the stable distribution.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.2, Problem 24E

Chapter 8.2, Problem 26E

Students have asked these similar questions

Calculate the following limit lim N→X [en] + [en] + n + [en]

Solve the given symbolic initial value problem and sketch a graph of the solution. y"+y=38 (1-2); y(0) = 0, y'(0) = 2

Solve the following system of equations: 50x+20y=1800 10x+3y=300

Chapter 8 Solutions

EBK FINITE MATHEMATICS & ITS APPLICATIO

Ch. 8.1 - 1. Is a stochastic matrix? Ch. 8.1 - 2. Learning Process An elementary learning process...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 4E Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 6E Ch. 8.1 - In Exercises 7–12, write a stochastic matrix...Ch. 8.1 - Prob. 8E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

To prove: The matrix [ 0.6 0 0.4 ] and [ 0.3 0.5 0.2 ] are both stable distributions for the stochastic matrix [ .4 0 .9 0 1 0 .6 0 .1 ] . Also, explain the reason due to which this fact does not contradict the uniqueness of the stable distribution.

Solution Summary: The author explains the stable distributions for the stochastic matrix left[cc.4& 0&

Concept explainers

Videos

To prove: The matrix [0.600.4] and [0.30.50.2] are both stable distributions for the stochastic matrix

[.40.9010.60.1]. Also, explain the reason due to which this fact does not contradict the uniqueness of the stable distribution.

Want to see the full answer?

Chapter 8 Solutions

To prove: The matrix [ 0.6 0 0.4 ] and [ 0.3 0.5 0.2 ] are both stable distributions for the stochastic matrix [ .4 0 .9 0 1 0 .6 0 .1 ] . Also, explain the reason due to which this fact does not contradict the uniqueness of the stable distribution.

Solution Summary: The author explains the stable distributions for the stochastic matrix left[cc.4& 0&

Concept explainers

Videos

To prove: The matrix [0.600.4] and [0.30.50.2] are both stable distributions for the stochastic matrix [.40.9010.60.1]. Also, explain the reason due to which this fact does not contradict the uniqueness of the stable distribution.

Want to see the full answer?

Chapter 8 Solutions

To prove: The matrix [0.600.4] and [0.30.50.2] are both stable distributions for the stochastic matrix

[.40.9010.60.1]. Also, explain the reason due to which this fact does not contradict the uniqueness of the stable distribution.