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  1. #1
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    statistics

    Let {Xi} be a sequence of independent draws from U(0,1) and let Y=X1+X2+...+Xn.
    i) Find the expected value of Y and the variance of Y
    ii) Find a function of Y that is asymptotically standard normal.
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  2. #2
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    Quote Originally Posted by trukka View Post
    Let {Xi} be a sequence of independent draws from U(0,1) and let Y=X1+X2+...+Xn.
    i) Find the expected value of Y and the variance of Y
    ii) Find a function of Y that is asymptotically standard normal.
    E(Y) = n/2
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  3. #3
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    Quote Originally Posted by trukka View Post
    Let {Xi} be a sequence of independent draws from U(0,1) and let Y=X1+X2+...+Xn.
    i) Find the expected value of Y and the variance of Y
    ii) Find a function of Y that is asymptotically standard normal.
    (i) You should know that:

    E(Y) = E(X1) + E(X2) + ..... + E(Xn)

    Var(Y) = Var(X1) + Var(X2) + ...... Var(Xn)


    (ii) The Central Limit Theorem is your friend.
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