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Math Help - variance problem (i think)

  1. #1
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    variance problem (i think)

    Sorry, I was having difficulty with the equation editor on here. I've attached my problem as a picture file.

    I need to show that the two equations are equal, and I'm not sure where to begin.

    Thanks!
    Attached Thumbnails Attached Thumbnails variance problem (i think)-problem-1.png  
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  2. #2
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    Assuming that \overline{z} is the conjugate of the complex number z, that statement is false.
    \overline{({z-\overline{z}})^2~}=\overline{z~}^2 -2\overline{z}z+z^2 .

    Note that  \overline{\overline{z}}=z and  \overline{z^2}=\overline{z}^2
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  3. #3
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    Quote Originally Posted by chemekydie View Post
    Sorry, I was having difficulty with the equation editor on here. I've attached my problem as a picture file.

    I need to show that the two equations are equal, and I'm not sure where to begin.

    Thanks!
    \overline{(x-\overline{x})^2}=\overline{x^2-2x\overline{x}+\overline{x}^2} =\overline{x^2}-2\overline{x}\overline{x}+\overline{x}^2

    etc.

    CB
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  4. #4
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    @Plato - x-bar is not a conjugate

    @CaptainBlack -

    In your process, what happens to the x double bar? How does that get factored out?
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  5. #5
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    Quote Originally Posted by chemekydie View Post
    @Plato - x-bar is not a conjugate

    @CaptainBlack -

    In your process, what happens to the x double bar? How does that get factored out?
    OK, then what is \overline{x}?
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  6. #6
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    Quote Originally Posted by Plato View Post
    OK, then what is \overline{x}?
    Expectation of x (the clue is in the thread title)

    CB
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  7. #7
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    Quote Originally Posted by chemekydie View Post
    @Plato - x-bar is not a conjugate

    @CaptainBlack -

    In your process, what happens to the x double bar? How does that get factored out?
    \overline{x} is just a number its expected value is itself :

    \overline{(\overline{x})}=\overline{x}

    CB
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  8. #8
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    x-bar is the mean.

    I was under the assumption that x double bar is the average of the means. I'm not aware that x double bar can be transformed back to regular x bar.

    Am I missing something?
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  9. #9
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    Quote Originally Posted by chemekydie View Post
    x-bar is the mean.

    I was under the assumption that x double bar is the average of the means. I'm not aware that x double bar can be transformed back to regular x bar.

    Am I missing something?
    x double bar as you call it is the mean of the mean, but the mean is just a number, its mean is itself.

    To see this just look at your definition of a mean.

    CB
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  10. #10
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    Quote Originally Posted by CaptainBlack View Post
    \overline{(x-\overline{x})^2}=\overline{x^2-2x\overline{x}+\overline{x}^2} =\overline{x^2}-2\overline{x}\overline{x}+\overline{x}^2

    etc.

    CB
    I'm getting a +\overline{x}^2 instead of negative. And I'm not sure how to factor out the 2.
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  11. #11
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    Quote Originally Posted by chemekydie View Post
    I'm getting a +\overline{x}^2 instead of negative. And I'm not sure how to factor out the 2.
    \overline{-2x\overline{x}}=-2\overline{x}~\overline{\overline{x}}=-2\overline{x}~\overline{x}=-2\overline{x}^2
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