(2) The long term steady state vector q is independent of the initial vector. To verify this statement, let's consider the same transition matrix P as in the weather example but use another initial vector of [0.5, 0.5] (the values must sum up to be 1). Follow the power method to approximate q. You may stop at X(7). Compare your answers with the following and select all the correct options. x(1) X(0) P = [0.7, 0.3] x(1) X(0) P = [0.6, 0.4] OX(2) = x(¹) P[0.68, 0.32] X(2)x(1) P = [0.78, 0.22] X(3) X(2) P = [0.712, 0.288] x(3) X(2) p = [0.812, 0.188] X(4) X(3) P[0.8248, 0.1752] X(4)= x(3) P = [0.7248, 0.2752] X(5) X(4) P = [0.82992, 0.17008] X(5) X(4) P = [0.72992, 0.27008] X(6) X(5) p [0.831968, 0.168032] X(6) X(5) p = [0.7327872, 0.2672128] X(7)x(6) p = [0.73311488, 0.26688512] X(7) X(6) P= [0.8327872, 0.1672128]

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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(2) The long term steady state vector q is independent of the initial vector. To verify this statement,
let's consider the same transition matrix P as in the weather example but use another initial vector of
[0.5, 0.5] (the values must sum up to be 1). Follow the power method to approximate q. You may
stop at X(7). Compare your answers with the following and select all the correct options.
U
U
U
U
x(1)
X(0) P = [0.7, 0.3]
x(1) X(0) P = [0.6, 0.4]
X(2) = x(1) p = [0.68, 0.32]
X(2) = x(1) p = [0.78, 0.22]
x(3) = x(2) p = [0.712, 0.288]
X(3) X(2) P [0.812, 0.188]
=
=
=
X(4) X(3) P = [0.8248, 0.1752]
=
X(4)= x(3) P = [0.7248, 0.2752]
X(5) X(4) P = [0.82992, 0.17008]
X(5) X(4) P = [0.72992, 0.27008]
=
X(6) X(5) p = [0.831968, 0.168032]
=
X(6)
=
X(5) p = [0.7327872, 0.2672128]
X(7) = x(6) p = [0.73311488, 0.26688512]
X(7)
X(6) p = [0.8327872, 0.1672128]
=
Transcribed Image Text:(2) The long term steady state vector q is independent of the initial vector. To verify this statement, let's consider the same transition matrix P as in the weather example but use another initial vector of [0.5, 0.5] (the values must sum up to be 1). Follow the power method to approximate q. You may stop at X(7). Compare your answers with the following and select all the correct options. U U U U x(1) X(0) P = [0.7, 0.3] x(1) X(0) P = [0.6, 0.4] X(2) = x(1) p = [0.68, 0.32] X(2) = x(1) p = [0.78, 0.22] x(3) = x(2) p = [0.712, 0.288] X(3) X(2) P [0.812, 0.188] = = = X(4) X(3) P = [0.8248, 0.1752] = X(4)= x(3) P = [0.7248, 0.2752] X(5) X(4) P = [0.82992, 0.17008] X(5) X(4) P = [0.72992, 0.27008] = X(6) X(5) p = [0.831968, 0.168032] = X(6) = X(5) p = [0.7327872, 0.2672128] X(7) = x(6) p = [0.73311488, 0.26688512] X(7) X(6) p = [0.8327872, 0.1672128] =
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