FOUNDATIONS OF THEORETICAL STATISTICS. 
335 
whence it follows, since n is large, that 
V = . H g+OT+6) = i (p +1) (p +2) (p +6). 
11 n p + ] n 
From the value of L, 
~ lo §' (p-) + s ( lo s -—— 
op dp \ a 
which equation solved for m, a and p as a simultaneous equation with (1) and (2), will 
yield the set of values for the parameters which has the maximum likelihood. To find 
the variance of the value of p, so obtained, observe that 
of which the mean value is 
i-U = -s f-A 
cm (p 
,c—m 
n 
ap 
and 
2 L 
da dp 
a 2 l 
n 
cd 
d 2 
a -a = -r- 2 log (p !). 
op dp 
The variance of p, derived from this set of simultaneous equations, is therefore found 
y2T 
by dividing the minor of , namely 
by the determinant 
n 
P 
— i a 
■i > 
n 
a 
hence 
__L_ | A 
P~ 1 P 
1 p +1 1 
1 
P 
I 
yu log iP '•) 
dp 
n 3 
- —— ! 2 -f- 2 log (p!) — - + K ;; 
a p—] I dp s v p p\ 
2 log (pi) - - + — !■ 
dp' p p I 
2 . 1 
. cZ 2 , , „ 2 1 
i (1 
When p is large, 
1 
1 
