Students " Probably Error of the Mean " written long ago Chose values for : ( A, n, Sigma ) in Purple to - " shape " Students Standard Deviation which is proved with all the Proper Mathematics in Student's Paper.
invented the Standard Deviation Curve which I finally understand it's existence ( Must adjust all three variables ) - n= 2 is good for a constant and is Cited in the Article mentioned below.
to adjust to other Distributions But: n = 3
that his Distribution fits most Distributions. n=4 without Changing " A or Sigma " will give a close approximation of My RV Sigma
for the Expected Value x*g(x) and x^2*g(x) which supports my equations theory!!!
The Probable Error of a Mean --- Refer to this Paper for the Purple Formula which I copied here to Explore.
Author(s): Student
Source: Biometrika, Vol. 6, No. 1 (Mar., 1908), pp. 1-25
Published by: Biometrika Trust
Stable URL: http://www.jstor.org/stable/2331554
Accessed: 11/12/2009 10:55
Set " n " = 2 , 3 , 4 A = .47 ; Sigma = 1 : Check Boxes to see comparison Distribution of RV Sigma to Student's.
Set: A =1.6 ; n = 2 ; Sigma = .35 -- Purple input Boxes