MAKE A MEME
View Large Image
| View Original: | Convergence in distribution (sum of uniform rvs).gif (200x148) | |||
| Download: | Original | Medium | Small | Thumb |
| Courtesy of: | commons.wikimedia.org | More Like This | ||
| Keywords: Convergence in distribution (sum of uniform rvs).gif en Z_n is a normalized sum of iid uniform random variables Z_n 1/ ˆšn Sum U -1 1 i 1 n The animation shows how the pdfs of Z_n converge to a normal N 0 …“ random variable own Stpasha Mathematica source <nowiki>fx_ If-1 < x < 1 1/2 0; f2x_ Evaluate\ \ \ SubsuperscriptBox\ \Integral\ \ -\Infinity\ \ \Infinity\ ft fx - t \DifferentialDt\ ; f3x_ Evaluate\ \ \ SubsuperscriptBox\ \Integral\ \ -\Infinity\ \ \Infinity\ ft f2x - t \DifferentialDt\ ; f4x_ Evaluate\ \ \ SubsuperscriptBox\ \Integral\ \ -\Infinity\ \ \Infinity\ ft f3x - t \DifferentialDt\ ; f5x_ Evaluate\ \ \ SubsuperscriptBox\ \Integral\ \ -\Infinity\ \ \Infinity\ ft f4x - t \DifferentialDt\ ; f6x_ Evaluate\ \ \ SubsuperscriptBox\ \Integral\ \ -\Infinity\ \ \Infinity\ ft f5x - t \DifferentialDt\ ; f7x_ Evaluate\ \ \ SubsuperscriptBox\ \Integral\ \ -\Infinity\ \ \Infinity\ ft f6x - t \DifferentialDt\ ; f8x_ Evaluate\ \ \ SubsuperscriptBox\ \Integral\ \ -\Infinity\ \ \Infinity\ ft f7x - t \DifferentialDt\ ; f9x_ Evaluate\ \ \ SubsuperscriptBox\ \Integral\ \ -\Infinity\ \ \Infinity\ ft f8x - t \DifferentialDt\ ; fnn_ x_ \Piecewise Sqrt1 f1Sqrt1 x n 1 Sqrt2 f2Sqrt2 x n 2 Sqrt3 f3Sqrt3 x n 3 Sqrt4 f4Sqrt4 x n 4 Sqrt5 f5Sqrt5 x n 5 Sqrt6 f6Sqrt6 x n 6 Sqrt7 f7Sqrt7 x n 7 Sqrt8 f8Sqrt8 x n 8 Sqrt9 f9Sqrt9 x n 9 Table Plotfnn x x -2 2 Exclusions -> None PlotRange -> 0 0 8 ImageSize -> 200 PlotStyle -> ThicknessLarge LabelStyle -> DirectiveLarger Epilog -> InsetStyle \ \ \ StyleBox\ n\ \nFontSlant->\ Italic\ \ <> ToStringn 18 1 2 0 75 n 1 9 1 Export c /anim gif DisplayDurations -> 1 1 1 1 1 1 1 1 25 TransparentColor -> White </nowiki> cc-zero Convergence | ||||
.gif){kind=link}
