Exercise Work out the 7²-statistic for all 26 shifts to see that shift 3 is really the best fit.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Question
Reconsider the example from po.
IDEA: We can do 26 7²-calculations to see which shift gives the
best goodness of fit with the usual distribution of letters in
an English text.
Observed
frequency
shift O
shift!
shift 2
3
2
2
2
O
4
4
4
8
I
1
3
S
2
O
4
4
2
2
5
5
4
4
2
2
2
2
4
Letter
ADCDEFYIMM XLINOPSISTOVAN
Expected frequency
in a text of 65
Symbols
5.30
0.89
1.44
2.98
8.20
1.21
1.53
4.45
4.53
0.09
0.70
2.84
1.27
S
4.24
4
૧, ૧૦
2
0.91
2
0.12
4
3.26
3.93
4
6.45
3
2.09
2
0.51
8
2
1.62
0
0
0.08
2
3
1.37
2
0.05
(0-5.3)²
(2-0.05)
(3-0.89)
0.89
(2-1.44)²
1.44
5.3
0.05
Work out the ²-statistic for all 26 shifts to see that shift 3
is really the best fit.
x² (shift o)
:
2² (shift 25)
Exercise
=
+
S
2
0
2
5
4
2
2
4
3
2
O
2
+
1
1
3
$
2
0
2
S
4
2
2
4
3
2
3
2
3
shift 3.
2
4
8
Transcribed Image Text:Reconsider the example from po. IDEA: We can do 26 7²-calculations to see which shift gives the best goodness of fit with the usual distribution of letters in an English text. Observed frequency shift O shift! shift 2 3 2 2 2 O 4 4 4 8 I 1 3 S 2 O 4 4 2 2 5 5 4 4 2 2 2 2 4 Letter ADCDEFYIMM XLINOPSISTOVAN Expected frequency in a text of 65 Symbols 5.30 0.89 1.44 2.98 8.20 1.21 1.53 4.45 4.53 0.09 0.70 2.84 1.27 S 4.24 4 ૧, ૧૦ 2 0.91 2 0.12 4 3.26 3.93 4 6.45 3 2.09 2 0.51 8 2 1.62 0 0 0.08 2 3 1.37 2 0.05 (0-5.3)² (2-0.05) (3-0.89) 0.89 (2-1.44)² 1.44 5.3 0.05 Work out the ²-statistic for all 26 shifts to see that shift 3 is really the best fit. x² (shift o) : 2² (shift 25) Exercise = + S 2 0 2 5 4 2 2 4 3 2 O 2 + 1 1 3 $ 2 0 2 S 4 2 2 4 3 2 3 2 3 shift 3. 2 4 8
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