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Stats question, how to get expected values

  1. Mar 21, 2012 #1
    1. The problem statement, all variables and given/known data

    I have taken a random sample such that X~N(8,2).

    I want to use the samples that I have generated to estimate E(xbar), E(s2), E(α21) and E(α22) for the population.

    2. Relevant equations
    3. The attempt at a solution

    I am not entirely sure how to do these.

    I know that for a random variable, E(x)= (x1 + x2 ... +xn)/n, but I am not sure if this is the same for a sample/xbar.

    I have googled and can't find the formulas, does anyone know them here?

    I know for s^2 that E(s^2) = E[{sum(i to n) (xi-xbar)^2}/(n-1)]

    so now I can bring the 1/(n-1) out front of the E, but I'm not sure how the summation acts.
     
    Last edited: Mar 21, 2012
  2. jcsd
  3. Mar 21, 2012 #2
    You are confusing some concepts. You want to estimate say, the mean of the random variable X μ=E{X}, you use the estimator [itex]\bar{x}=\frac{1}{N}\sum_nx_n[/itex] where x_n are the samples of X. You can prove [itex]E[\bar{x}]=\mu[/itex] so that the estimator which is a function of the samples has an expected value that is equal to the mean μ of X, so that this estimator is unbiased. Now try to find unbiased estimators of other parameters of the random variable X that you want to estimate, as a function of the samples, i.e., the expected values are equal to the parameters you want to estimate.
     
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