Rit (Vísindafélag Íslendinga) - 01.06.1931, Blaðsíða 42

42
or c~" {l2V+-f+~f+ -30 = - b(4’/+^+...)+C
(67a)
where
ai=a - 4
and
c=c—b4
From (67a) the following relations ensue:
ai+ci=0, ++bX2+ai=0, b4+4‘—2A2—ai=0
(b+l)?4—34+34+ai=0 etc.
whence we obtain:
4 - 4
b =
and
in that
242
4+4’ 1 4+4’
. A2 — 4 i 242
c=4 , -|"t +
4+4 4+4

v = /vy/2= n+\'h
4 14 / \ 4
(67b)
(67c)
where 4', 4'. 4' etc. are the semi-invariants computed
from the observations of the frequency distribution.
The probability resulting from (66) is:
y =f(x)
Cb“____
(x—a)! (|-x)!
(67d)
and the auxiliary equations (63) and (63a) evidence that the
limits are x = a and x = c b.
B. Let the probability be:
V = f(x^ = (68)
whence the difference equation:
(x —b+1) f (x+1) — af(x) = 0 (68a)
Its Laplacian transform is:
-b<7) _aö = 0
d V