Image:Central limit thm 1.png
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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:
Missing image Heckert_GNU_white.png | 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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