# General Report on Tunny

22K Page 72

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 nΘ. Some estimate of the S.D. of this sigma-age can be obtained from the numbers σΘ. 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 Pa + Pb is deducible from the frequency of letters in Pa by means of the Faltung Theorem (22E).

We can score a stream of letters suspected of being Pa + Pb. For each occurance of Θ in the stream we get a factor
 that is a decibanage of 10 log 10 {32(Pa + Pb) = 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
 ΔDa + ΔDb = ΔΨ'a + ΔPa + ΔΨ'b + ΔPb = ΔΨ'a + ΔΨ'b   (since ΔPa = ΔPb)