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Statistic that is unbiased for Sigma^2 + ^2

  1. Mar 5, 2012 #1
    μ1. The problem statement, all variables and given/known data

    Let X1...Xn be a random sample of size n from a normal distribution, Xi~N(μ, sigma^2), and define U = ƩXi and W = ƩXi^2.

    Find a statistic that is unbiased for δ^2 + μ^2 in terms of U and W.

    2. Relevant equations
    xbar (sample mean) = Ʃxi/n
    S^2 (sample variance)(Ʃxi^2 + n*xbar^2)/(n-1)

    3. The attempt at a solution
    The real answer is W/n. However I am getting (Wn^2 - U^2)/n^2(n-1) from plugging in the estimators. This worked for the parameter 2μ - 5δ^2. What do I need to do?
  2. jcsd
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