Image:P(m,26).svg

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P(m,26).svg‎ (720 × 720 pixel, file size: 109 KB, MIME type: image/svg+xml)

[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.

[edit] Licensing

I, the creator of this work, hereby release it into the public domain. This applies worldwide.
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(del) (cur) 20:46, 17 January 2006 . . Ilmari Karonen (Talk | contribs) . . 720×720 (111,594 bytes) (Sigh, rendering problems again.)
(del) (rev) 20:45, 17 January 2006 . . Ilmari Karonen (Talk | contribs) . . 720×720 (49,203 bytes) (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.)