60 
Choice in the Distribution of Observations 
We now have to determine y and so that the maximum value a'y is as small 
as possible. We find 
^_4(2a.^^a«».-J,,) (71, 
and 
Clearly 
dy 
dal 
x=l 
= ^[2ay+2a^yv^+a--^^ 
= 0 leads to y^ 
av^ (2 + av^) 
.(72). 
.(73). 
Introducing this value into (72) we obtain 
^=1 ^ V Va(2 + avy 
which is > 0. 
Hence the minimum for constant determined by 
dtr', 
decreases with r'^. 
dy 
= 0 
x=l 
But when decreases, y^, as given by (73), increases and the lowest value of v^, 
for which it is real, is that determined by 
1 
au" (2 + av^) 
1. 
For V" smaller than this (73) gives y^> 1, and as long as 5 1 we therefore 
have 
dal 
dy jx 
0. 
Hence the minimum of al is to be found for y^= 1. 
For this value (72) may be written as 
dal _ 
x=i~ N V 
dv^ 
which is zero for = — J + 
and > 0 for greater than this value. 
1+- 
16 
.(75) 
When the found lies between 0 and 1, that is when a > I, we have thus found 
dal 
the minimum sought. When a < 1- , then 
dv^ 
a;=l 
as given by (74) is <0 and the 
x=l 
minimum of al is found by giving its maximum value, that is 1. 
Returning to the variates fj.^ and fx^ we see that in all cases 
,2 _ 1 
^ ^2 ' 
