FFRank,

I'll simply point out in the case where there are only two states (0 and 1), your calculations devolve into calculations of binomials. There are formulas for these, they can be exactly calculated without brute forcing them. What you're looking at I'd call a multinomial formula, a "generalized" binomial formula. The formula probably can be found in a decent mathematical physics text or a text on statistical mechanics, or a higher end probability text. For that matter, the multinomial formula is given here.

This of course means what you're dealing with are factorial calculations as you scale up. I think you'll lose the ability to get exact answers rapidly, though the logarithmic form of Stirling's formula may allow you approximate answers on the high end of things.

David

Update: More exact language. Binomial coefficients aren't binomial distributions. Added a link to a multinomial formula.

In reply to Re: Probability sum of random variables by dwm042
in thread Probability sum of random variables by FFRANK

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.