Page:Biometrika - Volume 6, Issue 1.djvu/4

4 In a similar tedious way I find:

and

The law of formation of these moment coefficients appears to be a simple one, but I have not seen my way to a general proof.

If now $$M_R$$ be the $$R$$th moment coefficient of $$s^2$$ about its mean, we have

Hence

Consequently a curve of Professor Pearson’s type III. may be expected to fit the distribution of $$s^2$$.

The equation referred to an origin at the zero end of the curve will be

where

and

Consequently the equation becomes

which will give the distribution of $$s^2$$.

The area of this curve is $$C\int_0^\infty x^\frac{n-3}{2}e^{-\frac{nx}{2\mu_2}}dx=I$$ (say).