You must answer the following question (obviously leaving a trace of the calculations made to answer it): If we start at site 0 (therefore p0=1 and all the others pi=0), after how many steps n the probabilities pin are they all close to the asymptotic probabilities πi at most 0.001, ie |pin-πi|≤ 0.001? To answer this question, follow the following steps (see example in image). To be efficient, consider using incrementing, cell calling, etc. (a) On line 2, enter a step counter starting at step 0. (b) On lines 4 and following, indicate the vectors of probabilities pin, so step 0 corresponds to the initial vector, then in the next column, in the column identified by step 1, the vector of probabilities after a step , etc. (c) On lines 15 and following, check if the distance between pin and πi is smaller; in the step 0 column, line 15, indicate: "=ABS(A4-cell containing π0)<=0.001". Then increment (blocking the addresses to be) to check the distances between each pin. Finally, identify, by giving a color to the corresponding column, the first step from which all the distances between the pi^n and πi are all less than or equal to 0.001. π= 0.113821 0.043360 0.043360 0.048780 0.140921 0.157182 0.078591 0.086721 0.195122 0.092141

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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Excel

You must answer the following question (obviously leaving a trace of the calculations made to answer it): If we start at site 0 (therefore p0=1 and all the others pi=0), after how many steps n the probabilities p_iⁿ are they all close to the asymptotic probabilities π_i at most 0.001, ie |p_iⁿ-π_i|≤ 0.001? To answer this question, follow the following steps (see example in image). To be efficient, consider using incrementing, cell calling, etc.
(a) On line 2, enter a step counter starting at step 0.
(b) On lines 4 and following, indicate the vectors of probabilities p_iⁿ, so step 0 corresponds to the initial vector, then in the next column, in the column identified by step 1, the vector of probabilities after a step , etc.
(c) On lines 15 and following, check if the distance between p_iⁿ and π_i is smaller; in the step 0 column, line 15, indicate: "=ABS(A4-cell containing π₀)<=0.001". Then increment (blocking the addresses to be) to check the distances between each p_iⁿ. Finally, identify, by giving a color to the corresponding column, the first step from which all the distances between the pi^n and πi are all less than or equal to 0.001.

π=

0.113821
0.043360
0.043360
0.048780
0.140921
0.157182
0.078591
0.086721
0.195122
0.092141

SOMME
Modes d'affichage
A
Pas:
1
0
0
0
0
0
0
0
B
0
0
X
1
2
0
1
3 Vecteur de prob.:
4
0
5
0,5
6
0
7
0
8
0
9
0 0,16667
10
11
12
13
14 Différence avec Pi
15 0,001
16
17
18
0,5
с
0
0
0
fx
2
0,16667
0
0,25
0
=ABS(A4-Feuil1!D75)<=0,001
D
0,25 0,08333333
3
Afficher
0,16666667
0,08333333
E
4
F
5
Zoom
G
0,0625 0,11111111 0,14293981
0,125 0,22222222 0,28587963
6
H
no
7:
I
8
0,078125 0,11250965
0,15625 0,22501929 0,22640175
0 0,04166667 0,06018519 0,01967593 0,04552469
0,11111111 0,14293981
0,078125 0,11250965
0,0625
0 0,13888889 0,02777778 0,08101852
0,06635802 0,08121142
0 0,04166667 0,06018519 0,01967593 0,04552469 0,04594264
0
0,125 0,18055556 0,05902778 0,13657407 0,13782793 0,12027392
0 0,16666667
0 0,04166667 0,06018519 0,01967593
0
0,16667
0 0,04166667 0,06018519 0,01967593 0,04552469 0,04594264
0 0,41666667 0,08333333 0,24305556 0,19907407 0,24363426 0,19000772

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