- #1
iVenky
- 212
- 12
Let 'x' and 'y' be two random variables with zero mean.
We find that 'x' is related to 'y' with a correlation coefficient 'c'.
Now let us say we are splitting 'x' into correlated term 'xc'and uncorrelated term 'xu'
Then we have
[tex]
x= x_c + x_u
\\
\overline{x^2}= \overline{(x_c + x_u)^2} = \overline{x_c^2} + \overline{x_u^2}
[/tex]
Then does it mean the following is true? -
[tex]
\overline{x_c^2}= \overline{x^2}(|c|^2)
\\
\overline{x_u^2}=\overline{x^2}(1-|c|^2)
[/tex]
If so how would you prove it?
I am sure that the above result is true as I saw it in a book.
Thanks a lot
We find that 'x' is related to 'y' with a correlation coefficient 'c'.
Now let us say we are splitting 'x' into correlated term 'xc'and uncorrelated term 'xu'
Then we have
[tex]
x= x_c + x_u
\\
\overline{x^2}= \overline{(x_c + x_u)^2} = \overline{x_c^2} + \overline{x_u^2}
[/tex]
Then does it mean the following is true? -
[tex]
\overline{x_c^2}= \overline{x^2}(|c|^2)
\\
\overline{x_u^2}=\overline{x^2}(1-|c|^2)
[/tex]
If so how would you prove it?
I am sure that the above result is true as I saw it in a book.
Thanks a lot