A Nonstandard Standard
The normal curve with variance 1/2 has a tidy formula, f(x) = e^(−x²)/√π, but it isn't the usual standard normal. It's a nonstandard standard.
Transcript
[f(x) = (1/√π) e^(−x²) (when σ² = 1/2)] "This standard is kind of nice!" "But… it's not the standard…" "Well, it's a nonstandard standard."
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Free for classrooms, worksheets, slides and other non-commercial use under CC BY-NC 4.0, with credit to Ben Orlin.
Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2018-08-15-a-nonstandard-standard/ (CC BY-NC 4.0)