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Derivation of the probability distribution function of a binomial distribution

  1. Mar 26, 2006 #1
    Is there a way to derive

    [tex] P (X=r) =^nC_r p^r q^{n-r} , r= 0, 1, 2,...., n [/tex]

    where [tex] X: B(n,p) [/tex]

    where n is the total number of bernoulli experiments,

    p the probability of success

    q, the probability of failure.
  2. jcsd
  3. Mar 26, 2006 #2

    matt grime

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    Yes, just think about it, it's just simple combinatorics (you omitted to mention independent trials, which is, I'm sure important), and no harder than working out how to choose r from n (in fact it is the same).
  4. Mar 29, 2006 #3
    This is not a problem as matt goes into. Suppose we have XXX and YY,then how many ways can combinations occur? Well there are five elements in 5! ways, but 3 of them are similar and the other two are similar, so it's 5!/(3!2!)=10 distinct ways. YYXXX, YXYXX, YXXYX, YXXXY, XYXXY, XXYXY, XXXYY, XYYXX, XXYYX, XYXYX.
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