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Math Help - Help needed for Random Variable Stat Question

  1. #1
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    Help needed for Random Variable Stat Question

    here is the question im not sure how to go about doing it

    We know that for any random variable Y, the variance of Y is defined as
    σY2 = E(Y-E(Y))2 = E(Y2) [E(Y)]2

    a) Apply this formula to the sample mean of a random sample of size n from a population with mean μ and variance σ2, and show that
    E( 2) = μ2 + σ2/n


    Thanks guys
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  2. #2
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    Quote Originally Posted by flaming View Post
    here is the question im not sure how to go about doing it

    We know that for any random variable Y, the variance of Y is defined as
    σY2 = E(Y-E(Y))2 = E(Y2) [E(Y)]2

    a) Apply this formula to the sample mean of a random sample of size n from a population with mean μ and variance σ2, and show that
    E( 2) = μ2 + σ2/n


    Thanks guys
    n(E(Y^2)-\mu^2)=\sigma^2

    There is n random Y variables, hence the expectation is multiplied like so.
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  3. #3
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    hey

    umm can u explain to me the second part of this question im not sure when it is biased or not.

    the second part is

    : Is (Xbar^2) an unbiased estimator of μ2. Explain. If it is biased, what is the bias of this estimator?
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