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since the expected value of the modulus of the deviation from the mean is so σ in the case of normal variate. Of course this is not accurate, but accuracy is not the point.
The expected sigma-age of a chi run (See 23C(d)) can be worked out sufficiently accurately from the average letter count, i.e. the 32 numbers n_{Θ}. Some estimate of the S.D. of this sigma-age can be obtained from the numbers σ_{Θ}. A very crude method of doing this is given in R2, 56, 60, 61 and pp. 17, 21 of the note-book 'Alphabetical counts and runs statistics'.
22W SOME FURTHER STREAMS
(a) The Sum of two P-Streams.
The frequency of letters in P_{a} + P_{b} is deducible from the frequency of letters in P_{a} by means of the Faltung Theorem (22E).
We can score a stream of letters suspected of being P_{a} + P_{b}. For each occurance of Θ in the stream we get a factor
that is a decibanage of 10 log _{10} {32(P_{a} + P_{b}) = Θ} |
(W1) |
The following table gives the centiban scores actually used in Room 41 for scoring suspected depths.
Θ Score | Θ Score | Θ Score | Θ Score |
/ +31 9 -1 H -12 T -16 O +7 M +1 N -17 3 +4 |
R -15 C -1 V +7 G +2 L -24 P -4 I -1 4 +10 |
A -2 U +11 Q -12 W -1 5 +3 8 +2 K -3 J +6 |
D -2 F +2 X -2 B -14 Z -4 Y -3 S +17 E -12 |
Fig. 22(XIV)
(b) The sum of two extended psi-streams.
Given two stretches of de-chi (a, b) which are known to have the same decode (as in an overlape) it is often possible to find the relative position of the P in the two stretches. For when set correctly
ΔD_{a} + ΔD_{b} = | ΔΨ'_{a} + ΔP_{a} + ΔΨ'_{b} + ΔP_{b} | |
= | ΔΨ'_{a} + ΔΨ'_{b} (since ΔP_{a} = ΔP_{b}) |
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