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I was studying some examples of linear correlations where I got the reasoning:

Since $X_,\;Y$ are measured from their means, $$E[X]= 0=E[Y]$$ ....

Can anyone tell me why it is so?

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    What does "measured from their means" mean? – sinbadh Jan 02 '16 at 12:57
  • Now, if I had known, would I have raised this question? I'm really in the blues. –  Jan 02 '16 at 13:02
  • Can you give more information about the context? Is it about linear (regression) models and if so, is $X$ random? – Nigel Overmars Jan 02 '16 at 13:03
  • @Nigel Overmars: There is really no more info actually:( I can only post that example-question, which, IMO, is unrelated to the line used in the reasoning. –  Jan 02 '16 at 13:21

2 Answers2

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To see what "measured from the means" means, consider the following example. Let $X$ be the random variable that measures the temperature in a place with mean temperature $E[X]=20^o$C. Let the temperature be $X=21$ at some given day. You can either write $X=21^o$ or $X=21-20=1$. In the second case you "measure $X$ from its mean". Similarly $X=19^o$ can be written as $X=-2$ etc. So, you use a new variable $$X'=X-μ$$ where $μ=Ε[Χ]$. Obviously $$E[X']=E[X-μ]=E[X]-E[X]=0$$ Τo avoid unnecessary notation, the author does not denote this new variable with $X'$ and just says that $X$ is "measured from its mean". Similarly for $Y$. You may also encounter the term "centered random variables". It is the same.

Jimmy R.
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I think means than the axis is centerded on their means. Think about if we know the mean of a r.v. we can center the r.v. by substracting the mean.

SNR
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