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Homework Help: Finding the MME for p of Bin(n,p)

  1. Mar 31, 2012 #1
    1. The problem statement, all variables and given/known data

    X1,X2,...,Xk ~iid Bin(n,p) find the MME (Method of Moments Estimator) for p

    2. Relevant equations

    E[X] = n⋅p
    Var[X] = n⋅p⋅(1-p)

    Var(X) = E[X2] - [E[X]]2

    3. The attempt at a solution

    Does this look correct?

    n⋅p⋅(1-p) = E[X2] - n2⋅p2

    E[X2] = n⋅p⋅(1-p) + n2⋅p2


    [itex]\bar{X}[/itex]2 = n⋅p⋅(1-p) + n2⋅p2

    [itex]\bar{X}[/itex]2 = [itex]\bar{X}[/itex]⋅(1-p) + [itex]\bar{X}[/itex]⋅[itex]\bar{X}[/itex]

    [itex]\hat{p}[/itex] = (([itex]\bar{X}[/itex])2 + [itex]\bar{X}[/itex] - [itex]\bar{X}[/itex]2) / [itex]\bar{X}[/itex]

    Last edited: Mar 31, 2012
  2. jcsd
  3. Mar 31, 2012 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    I'm not sure what "MME" stands for; In have seen the terms MMSE, MLE, etc., but not MME. Anyway, do you want to take the sample mean [tex] \bar{X} = \frac{\sum_{i=1}^k X_i}{k}?[/tex] If so, do you want [itex] E (\bar{X}) \text{ and } \text{Var}( \bar{X})?[/itex] If that is what you want to get, just use standard formulas for the mean and variance of [itex] \bar{X}[/itex] in terms of the means and variances of the [itex] X_i . [/itex] You will get formulas very different from what you wrote (although I must admit I do not know exactly what you were trying to do).

  4. Mar 31, 2012 #3
    MME := Method of Moments Estimator
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