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Math Help - Parameter estimation

  1. #1
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    Parameter estimation

    Let X_1,X_2,...,X_n be iid Bernoulli(p). Also let T be Binomial(n, p).

    So I found that they both have the same moment generating function, and I found the mean and variance of T. The question asks:

    Let n=20 and (x_1+...+x_n)=9. Using the method of moments, find an estimate of theta = log(p/(1-p)).

    I'm not sure how to proceed from here.
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  2. #2
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    Quote Originally Posted by BrownianMan View Post
    Let X_1,X_2,...,X_n be iid Bernoulli(p). Also let T be Binomial(n, p).

    So I found that they both have the same moment generating function, and I found the mean and variance of T. The question asks:

    Let n=20 and (x_1+...+x_n)=9. Using the method of moments, find an estimate of theta = log(p/(1-p)).

    I'm not sure how to proceed from here.
    With method of moments, the game is to equate the empirical moments with the theoretical moments. Set Xbar = p, then just plug that in to get the estimate of theta.
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  3. #3
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    So would the answer be -0.08?
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  4. #4
    MHF Contributor matheagle's Avatar
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    use p-hat as 9/20 to estimate p in theta

    ln (.45/.55)
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  5. #5
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    Thanks, I got it!

    The next part of the question which I'm not sure of is:

    Obtain a 95% confidence interval for theta based on the MLE of theta.
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