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Math Help - Sample mean and variance

  1. #1
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    Sample mean and variance



    \bar x_{n+1} = \frac{1}{n+1} \sum^{n+1}_{k=1} x_k ...and then, I'm stuck. No idea what to do next.
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  2. #2
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    Quote Originally Posted by cirrus74 View Post


    \bar x_{n+1} = \frac{1}{n+1} \sum^{n+1}_{k=1} x_k ...and then, I'm stuck. No idea what to do next.
    (a) \bar x_{n} = \frac{1}{n} \sum^{n}_{k=1} x_k \Rightarrow \sum^{n}_{k=1} x_k = n \bar x_{n}.

    Therefore:

    \sum^{n+1}_{k=1} x_k = \left( \sum^{n}_{k=1} x_k \right) + x_{n+1} = n \bar x_{n} + x_{n+1}.

    Therefore \bar x_{n+1} = \frac{n \bar x_{n} + x_{n+1}}{n+1}.


    You should have another go at (b) now ....
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