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Math Help - Efficiency

  1. #1
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    Efficiency

    Could anyone help with this?

    If X1, X2, and X3 constitute a random sample of size n=3 from a normal population with the mean m and the variance s2, find the efficiency of (X1+2X2+X4)/4 relative to (X1+X2+X3)/3.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by math beginner View Post
    Could anyone help with this?

    If X1, X2, and X3 constitute a random sample of size n=3 from a normal population with the mean m and the variance s2, find the efficiency of (X1+2X2+X4)/4 relative to (X1+X2+X3)/3.
    T_1=(X_1+2X_2+X_3)/4 and T_2=(X_1+X_2+X_3)/3 are unbiased estimators for \mu. (As can be seen since E(T_1)=\mu and E(T_2)=\mu )

    Then the relative efficiency e(T_1,T_2) of T_1 and T_2 is:

    e(T_1,T_2)=\frac{E((T_2-\mu)^2)}{E((T_1-\mu)^2)}

    CB
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