1) Normal Pink
2) Normal Standard Deviation Blue
3) RV Sigma Green
I have been looking at the paper written long ago, entitled " Probably error of the Mean " by Student. He derives the Standard Deviation in full with all the proper Math. His formula
can model any Distribution and in fact models both these two Distributions when n = 2 while adjusting " A " the constant and Sigma to model both distributions.
My formula is only one of many that can be derived. I did have right that Tan-1 = Z.