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Sufficient Estimator for a Geometric Distribution

  1. Jan 12, 2010 #1
    1. The problem statement, all variables and given/known data

    Let X1,..,Xn be a random sample of size n from a geometric distribution with pmf [tex]P(x; \theta) = (1-\theta)^x\theta[/tex]. Show that [tex]Y = \prod X_i[/tex] is a sufficient estimator of theta.

    2. Relevant equations



    3. The attempt at a solution

    So [tex]\prod P(x_i, \theta) = (1-\theta)^{\Sigma x_i} \theta^n[/tex]

    I don't believe that the factorization theroem can be applied here. Is there some trick to this that I'm not seeing?

    Thank you in advance.
     
  2. jcsd
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