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Unbised estimator of Binomial Distribution

  1. Sep 29, 2007 #1
    [SOLVED] unbised estimator of Binomial Distribution

    I have no idea how to find such an estimator
    Suppose[tex]X_1, ..., X_n \sim Bern(p)
    [/tex]
    find an unbiased estimator of [tex]p^m, for m < n[/tex]
    Induction on m was a nasty mess that should not be expected. The power of m causes some problem when I try to go from the definition of expectation. Any one have some hint?
     
  2. jcsd
  3. Sep 30, 2007 #2

    EnumaElish

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    Statistic u is unbiased if E = p^m. Suppose m = 2. To find u, you count all sequences that have two successes in a row, then express them as a ratio of the total number of trials. Would that satisfy E = p^2?
     
  4. Sep 30, 2007 #3
    I approached in a similar way.
    It is clear that [tex] Y = X_1....X_m [/tex] is unbiased for p^m. I was asked to find an unbiased estimator that is a function of sample total. Thus I construct a R.V which
    [tex] Z(T) = 1 for T = 26; 0 elsewhere[/tex]
    I might have to normalise Z so that it is the same as Y. However I dont know how to sum it.
     
  5. Sep 30, 2007 #4

    EnumaElish

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    Where did 26 come from?

    If you look at my previous post you will see that it is a function of the sample total.
     
  6. Sep 30, 2007 #5
    it is not 26, it should be m.....
     
  7. Sep 30, 2007 #6

    EnumaElish

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    Very well, my previous post applies.
     
  8. Sep 30, 2007 #7
    k gotcha thx
     
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