![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.
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.)](http://www.tumblr.com/photo/1280/isomorphismes/615407591/1/tumblr_l2peow4jCW1qc38e9)
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.
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.)
