Difference Problem 395 
Write x—sx', then, \i ys=y' 
Xv 
Hence dropping dashes we have : 
a= \ y dx', 
J -GO 
a'^-P{l-a)Pdx' (xi). 
n j -00 sl2 
n-lp /2 r™ -ix' J , --s 
or: ^ = A, / ~ I e - (xii). 
n V 77 j 0 
Thus as soon as n and p are known in can be found from tables of the probability integral. 
Then we may find from 
y,„ = -^e-^'"^ (xiii), 
VZTT 
or tables of the ordinates of the normal curve. 
We easily find by differentiating (xiii) that : 
y'm = - my^ , y",„ = {m' - 1 ) y,„ , y"'m = m{^-m^)y^ 
I/"m = {^ - 6m2 + »i*)^y,„, 7/\n = m {lOm^ - 15 - m*) j/„, (xiv). 
Substituting in (x) we find : 
— 
— + (xv). 
- 10n3 - r-^il (5'"' - 2) fm + + ^1 m (Sm^ - 5)/,„ . . .(xviii). 
■ n"- (- + (31m* - 101m2 + 28) (xix). 
\p n — p 
If the a's be found from these equations, then by (xi) and (vi) : 
\n {n—pY p'' I /{n—p)p 1 
= S 1 v27r \/ 5 
\n — p \p n" » Ji-* ?/„i 
42—2 
