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Unbiased estimator of a probability?

  1. Apr 1, 2010 #1
    Say, [tex]x_1{}[/tex]... [tex]x_n_+_1{}[/tex] are iid Bernoulli random variables with parameter p.

    I want an unbiased estimator for probability Pr([tex]\Sigma_{}[/tex] [tex]x_1_._._._n{}[/tex] > [tex]x_n_+_1{}[/tex] )

    I have failed to establish E(1 - [tex]\Pi[/tex] [tex]x_i{}[/tex]) is unbiased estimator for the probability.

    Any hints? thanks.
    Last edited: Apr 1, 2010
  2. jcsd
  3. Apr 8, 2010 #2


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    Note that (1) a sum of Bernoullis is Binomial, and (2) a Bernoulli is a special case of Binomial. So your probability becomes the probability of the difference between two Binomials, one with n trials and one with a single trial, being greater than zero, Bi(n) - Bi(1) > 0.
  4. Apr 8, 2010 #3
    Thanks I haven't thought about this view point.
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