## Central Limit Theorem

A nice illustration of the Central Limit Theorem by convolution.

**in R:**

`Heaviside <- function(x) { ifelse(x>0,1,0) }`

HH <- convolve( Heaviside(x), rev(Heaviside(x)), type = "open" )

HHHH <- convolve(HH, rev(HH), type = "open" )

HHHHHHHH <- convolve(HHHH, rev(HHHH), type = "open" )

etc.

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What I really like about this *dimostrazione* is that it’s not a proof, rather an experiment carried out on a computer.

This empiricism is especially cool since the Bell Curve, 80/20 Rule, etc, have become such a religion.

**NERD NOTE:** Which weapon is better, a **1d10** longsword, or a **2d4** oaken staff? Sometimes the damage is written as **1-10** longsword and **2-8** quarterstaff. However, these ranges disregard the greater likelihood of the quarterstaff scoring **4,5,6** damage than **1,2,7,8**. The longsword’s distribution **1d10 **~Uniform[1,10], while **2d4** looks like a **Λ**.

(To see this another way, think of the combinatorics.)

Tags: 80/20 rule, basic facts, basic_facts, central limit theorem, econometrics, facts, law of large numbers, math, mathematics, maths, normal curve, Oliver Heaviside, Pareto principle, probability, r, science, statistical analysis, statistics, Vilfredo Pareto

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