No σ for you!

[Albert Chan]

(11-25-2024 04:49 PM)carey Wrote:  \[
Gaussian function = f(x) = \frac{1}{\sqrt{2 \pi \sigma^2}} \exp\left(-\frac{(x - \mu)^2}{2 \sigma^2}\right),
\]

OT, I find standard normal (µ=0, σ=1) less confusing.
Above f(x) has unit of 1/σ, but pdf(z) is dimensionless.

pdf(z) := exp(-z*z/2) / sqrt(2*pi)      , where z = (x-µ)/σ

Dimensionless equation is better. More compact, and *only* 1 shape
We have a rough idea of probability without calculations, 68–95–99.7 rule

Also, with standard normal, we can solve for missing µ, σ