Image:P(m,26).svg

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P(m,26).svg‎ (SVG file, nominally 720 × 720 pixels, file size: 109 KB)

[edit] Summary

A plot of $P(m,n) = \sum_{k=0}^{n} (-1)^k {n \choose k} \left( \frac{n-k}{n} \right)^m$ for n = 26 and 0 ≤ m ≤ 200, i.e. the probability than m uniformly distributed random letters will contain the entire 26-letter alphabet. Computed with a Perl script given here, plotted with GNU Plotutils, tweaked in Inkscape.

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File history

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	Date/Time	Dimensions	User	Comment
current	20:46, 17 January 2006	720×720 (109 KB)	Ilmari Karonen (Talk \| contribs)	(Sigh, rendering problems again.)
	20:45, 17 January 2006	720×720 (48 KB)	Ilmari Karonen (Talk \| contribs)	(A plot of <math>P(m,n) = \sum_{k=0}^{n} (-1)^k {n \choose k} \left( \frac{n-k}{n} \right)^m</math> for ''n'' = 26 and 0 ≤ ''m'' ≤ 200.)