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Math Help - Help with Independent Random Variables question

  1. #1
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    Help with Independent Random Variables question

    Let
    X1, ,Xn be independent random variables with E(Xi) = μ and V (Xi) = sigma^2. Also,let X be the sample mean. Then Cov(Xi X , X) = c. What is the numerical value of c ? (Your answer should not depend on n, μ, or sigma)

    I have no clue how to do this question...any help will be greatly appreciated!

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  2. #2
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    Hello,

    Cov(X_i-\bar X,\bar X)=Cov(X_i,\bar X)-Var[\bar X]

    The variance is easy since they're all independent (hence the variance of their sum is the sum of their variance)

    Cov(X_i,\bar X)=\frac 1n \left[Cov(X_i,X_i)+\sum_{j\neq i} Cov(X_i,X_j)\right]=\frac{\sigma^2}{n}
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