# Thread:

1. ## 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

2. 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 $\overline{z^2}=\overline{z}^2$

3. Originally Posted by chemekydie
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

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

@CaptainBlack -

In your process, what happens to the x double bar? How does that get factored out?

5. Originally Posted by chemekydie
@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 $\overline{x}?$

6. Originally Posted by Plato
OK, then what is $\overline{x}?$
Expectation of $x$ (the clue is in the thread title)

CB

7. Originally Posted by chemekydie
@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

8. 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?

9. Originally Posted by chemekydie
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

10. Originally Posted by CaptainBlack
$\overline{(x-\overline{x})^2}=\overline{x^2-2x\overline{x}+\overline{x}^2}$ $=\overline{x^2}-2\overline{x}\overline{x}+\overline{x}^2$

etc.

CB
I'm getting a $+\overline{x}^2$ instead of negative. And I'm not sure how to factor out the 2.

11. Originally Posted by chemekydie
I'm getting a $+\overline{x}^2$ instead of negative. And I'm not sure how to factor out the 2.
$\overline{-2x\overline{x}}=-2\overline{x}~\overline{\overline{x}}=-2\overline{x}~\overline{x}=-2\overline{x}^2$
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 17, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.962039053440094, "perplexity_flag": "middle"}