cumsum ( rnorm(50), lend="butt", lwd=12, type="h" )

Cumulative sum of 50 draws from a normal distribution.

File this under mysteries of the Central Limit Theorem.

√π sqrt[pi]

π of course is the distance around a circle. √π is the area under ∫exp (−x²), and exp (−x²) is the key ingredient in the normal distribution.

That’s more or less what √π means—the area under the Bell curve.

But what does it mean mean? I mean, if π is a distance and √ is used to turn areas into distances — is it, like, shrinking the π even one more time? Are we talking about a half-dimension here?

edit: hmm, the end of this post seems to have been deleted by the rare weirdness of tumblr’s mass editor. I’ll see if I can’t remember how it ended. Umm, something about the moment-generating function? (i.e. going around the complex unit circle)

(A Lévy-Pareto process has infinite variance.) comptes_rendus_28 Cauchy distribution has infinite variance as contrasted to… Gaussian distribution which shoots down REAL fast: fast.

original Mandelbrot article on cotton prices as a Levy process