Abstract
If a series
u
1
,
u
2
,...
u
2n + 1
constitute a random sample from a normally distributed population, they any linear function A = S
1
2n + 1
(
a
r
u
r
) will also be normally distributed; moreover its mean will be zero if S(
a
r
) = 0, and its variance will be equal to that of the original population if S (
a
r
2
) = 1. Any other liner function B = S
1
2n + 1
(
b
r
u
r
) will be distributed independently of the first if S(
a
r
b
r
) = 0, and in this case the sum of the squares,
x
= A
2
+ B
2
, will be distributed so that the chance of exceeding any particular value of
x
is
e
-x/e
, where c is the mean value of x, equal to twice the variance of the population sampled.
Cited by
578 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献