Image:Central limit thm 1.png

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Central_limit_thm_1.png‎ (4KB, MIME type: image/png)

illustration of central limit theorem, part 1

I created these images: Image:Central_limit_thm_1.png, Image:Central_limit_thm_2.png, Image:Central_limit_thm_3.png, Image:Central_limit_thm_4.png. I license these images under the GFDL:

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
Subject to disclaimers.

Here are the GNU Octave commands to create these images:

dx = 0.002;
x1 = (1:1000)*dx;
p1 = [1:2:1000, 500*ones(1, 500)];

p1 = p1 / (sum(p1)*dx);
m = sum (x1.*p1)*dx;
x1 = x1 - m;
s = sqrt (sum ((x1.^2).*p1)*dx);
dx1 = dx/s;
x1 = x1/s;
p1 = p1*s;

p2 = conv (p1, p1) * dx1;
nx1 = length(x1);
x2 = [x1+min(x1) x1(2:nx1)+max(x1)];

p3 = conv (p2, p1) * dx1;
x3 = [x2+min(x1) x1(2:nx1)+max(x2)];

p4 = conv (p3, p1) * dx1;
x4 = [x3+min(x1) x1(2:nx1)+max(x3)];

p2 = p2 * sqrt(2);
x2 = x2 / sqrt(2);
dx2 = dx1 / sqrt(2);

p3 = p3 * sqrt(3);
x3 = x3 / sqrt(3);
dx3 = dx1 / sqrt(3);

p4 = p4 * sqrt(4);
x4 = x4 / sqrt(4);
dx4 = dx1 / sqrt(4);

sum (p1) * dx1
sum (p1.*x1) * dx1
sum (p1.*x1.^2) * dx1

sum (p2) * dx2
sum (p2.*x2) * dx2
sum (p2.*x2.^2) * dx2

sum (p3) * dx3
sum (p3.*x3) * dx3
sum (p3.*x3.^2) * dx3

sum (p4) * dx4
sum (p4.*x4) * dx4
sum (p4.*x4.^2) * dx4

axis ([-5 5 0 0.5])

gset nokey
gset terminal png

gset output 'central_limit_thm_1.png'
plot (x1, p1, 'r-')

gset output 'central_limit_thm_2.png'
plot (x2, p2, 'r-')

gset output 'central_limit_thm_3.png'
plot (x3, p3, 'r-')

gset output 'central_limit_thm_4.png'
plot (x4, p4, 'r-')

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