Re: Is there a natural phenomena which defines the Normal Curve?
> What simple dice experiment/coin toss experiment/etc. has a mean of
> zero and a std. dev. of 1? What's the proof of the normal curve?
Marginal probabilty dy/dx is negative of product x and y, normalized to
std. deviation sigma and vanishing at x = 0 and infinity. Marginal
probability ( as used in economics ... derivative or slope) is extremum
at an intermediate normally probable value x = sigma.
dy/dx = - x * y / sigma^2 ; y/ymax = e^ - ( x/sigma)^2/ 2 ;
Also d^2 y /d x^2 = y /sigma^2 ( (x/sigma)^2 -1) . Normal x =sigma
keeps probability linear, avoids monotonic ( x >> sigma) and
oscillatory tendency ( x << sigma).
.
Relevant Pages
- Re: weighted regression
... Probability theory gives you the answers, ... distribution that describes the possible measured y values give their ... Unfortunately these measurements were 'noisy', ... probability of a and b do not depend on the x's or sigma. ...
(sci.stat.math) - Re: six sigma & 99.99
... why people keep saying that Six sigma is 99.99 or Six sigma has a ... normal distribution beyond 4.5 sigma from the mean is indeed 3.4 parts ... probability distribution that has a finite standard deviation, ... than 6 standard deviations from the mean in a particular direction is at most ...
(sci.math) - Re: six sigma & 99.99-correction
... why people keep saying that Six sigma is 99.99 or Six sigma has a ... AFAIK in particle physics one keeps to the convention that if and when pictures of a conjectured newly observed phenomenon stand apart 5 times the standard deviation from more or less similar pictures, then one has a real discovery at hand. ... With "probability of 99.99" I guess you mean 99.99%? ... (Figures quoted from the Wikipedia page mentioned above; calculations were done to 12 significant decimal digits, but not all significant digits were written down in this post) ...
(sci.math) - Re: six sigma & 99.99-
... why people keep saying that Six sigma is 99.99 or Six sigma has a ... AFAIK in particle physics one keeps to the convention that if and when pictures of a conjectured newly observed phenomenon stand apart 5 times the standard deviation from more or less similar pictures, then one has a real discovery at hand. ... With "probability of 99.99" I guess you mean 99.99%? ... to a confidence level of 99.99% corresponds 3.89Sigma; ...
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