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Variance homework

  1. Jan 23, 2007 #1
    How do I approach finding variance of sample mean of Poisson distribution?
    thanks.
     
  2. jcsd
  3. Jan 23, 2007 #2

    radou

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    You can certainly start with looking at the definition of variance.
     
  4. Jan 23, 2007 #3
    I did: Var(X) = E(X2) - (E(X))2
    the problem is that this is given for rv X, not X' or X-bar, that's where i get lost.
    I know that last term is lambda2.
    Actually what I need to find for this problem is E(X'2), i.e.
    E(X'2) = Var(X') + lambda2
     
    Last edited: Jan 23, 2007
  5. Jan 23, 2007 #4
    ok, last question, pleeeease some one look :redface: i can't find much on this anywhere and the book does not say much... i don't have intuition for these things....
    can I say that sample variance is sum(lambda)/n?
    I found something that said sample variance is Sum(Var[X]) of whatever it is the RV divided by n....
     
    Last edited: Jan 23, 2007
  6. Jan 27, 2007 #5

    radou

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    According to my old lecture notes, the sample variance for (X1, ..., Xn) is defined with [tex]\frac{1}{n} \sum_{i=1}^n(X_{i}-\overline{X})^2[/tex], where [tex]\overline{X} = \frac{1}{n}\sum_{i=1}^n X_{i}[/tex] , and, in your case X~P(lambda).
     
  7. Jan 27, 2007 #6

    HallsofIvy

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    Yes, the Poisson distribution depends on a single parameter and has the property that both mean and standard distribution are equal to that parameter.
     
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