Frequency Arrays, Illustrating the Use of Logical Symbols in the Study of Statistical And Other Distributions

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for Oj, /?!... ao ... etc.
If it is required to find the various power and product moments, in sampling, of the higher moments, vice the means of the simple measures, of characters, the formulae will give these, since powers of measures maj- be taken as the characters considered. Arrays are very simply referred to means, viz. by suppressing the linear terms in their exponential expression [see (39), (40) e.g.].
Looking at the kind of result recorded in the problems dealt with in this chapter th
...e difficulties are realized that are likely to be encountered in attempting to obtain the terms contributing to the higher moments of this class of distributions in any piecemeal way instead of as a whole.
V. GEOMETRICAL DISTRIBUTIONS. SAMPLES OF VECTORS.
RANDOM MIGRATION 1. The symbols A, B, C ■.., which, hitherto, have symbolised unit characters generally, may as a special case stand for unit steps or vectors in given directions. JC, Y, Z may conveniently signify unit vectors parallel to the coordinate axes and, then, according to pre.sent methods, X-'- will present a step, parallel to the axis of .r, of x units and X'^'Y^Z'' will present the point whose coordinates are x, y, z relative to the origin.


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