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Binomial distribution

  1. Mar 30, 2014 #1
    The average if the binomial distribution with probability k for succes is simply:

    <> = Nk

    So this means that if <> = 1 the distribution function must be peaked around 1. In general when is it a good approximation (i.e. when is the function peaked sufficiently narrow) to say that the probability in N tries to have one or more succeses is simply:

    P(≥1) = Nk

    this obviously does not hold for Nk>1 but on the other hand I don't expect it to hold for small N. So my guess is when Nk is sufficiently small. Is that correct?
  2. jcsd
  3. Mar 31, 2014 #2


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    P(at least one success) = 1 - P(all failure) = 1 - (1-k)N.
    You should be able to analyze it.
  4. Apr 1, 2014 #3
    Right so using the binomail theorem you find:

    P(at least one success) = Nk - K(N,2)k2 + K(N,3)k3 - K(N,4)k4 + ....

    So the question is when the first term dominates. Im guessing for sufficiently small k?
  5. Apr 1, 2014 #4


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    You need Nk small, not just k. In your expression you seem to have extraneous K (capital k) from the second term on.
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