1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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]=n⋅p

    [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]

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

    Ray Vickson

    User Avatar
    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).

    RGV
     
  4. Mar 31, 2012 #3
    MME := Method of Moments Estimator
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Finding the MME for p of Bin(n,p)
  1. |P(N)| = |Reals| (Replies: 1)

  2. Evaluate ord_p(p^N!) (Replies: 2)

Loading...