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Math Help - Statistics

  1. #1
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    Statistics

    (a) Find the maximum- likelihood estimator for u, the population mean, given a sample of size n from a population with f(x) = 1/B, 0<x<B. Estimate B by the method of moments.

    (b)The sample 1.3,0.6,1.7,2.2,0.3,1.1 was drawn from a population with the density f(x) = 1/B, 0<x<B. What are the maximum-likelihood estimates of the mean and variance of the population?
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  2. #2
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    so far i know that

    f(x) = (1/B) ^n

    ln f(x) = n (1/B)

    d ln f(x)/ dB = -n/B^2

    any suggestions on where i went wrong?
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  3. #3
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by maurisa View Post
    so far i know that

    f(x) = (1/B) ^n

    ln f(x) = n (1/B)

    d ln f(x)/ dB = -n/B^2

    any suggestions on where i went wrong?
    you can't differentiate this. You need to include the indicator function, that the max is less than B.
    Since the likelihood function is B^{-n} I(\max X_i\le B) the max occurs when B is as small as possible
    which happens when B is the largest order statistic. Since the MLE of B is the largest order stat and the mean is B/2
    I guess the estimate you want is the max over 2.
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