Correlation of Two Random Vectors

[OhMyMarkov]

Hello everyone!

I'm coming to notice day by day how our education is purely focused on memorizing and applying formulas rather than understanding the concept. Assume we have the following:

$X = aR + N$, and
$Y = bG + W$,

where $X, Y$ are random vectors, $R, G$ are strongly correlated random vector that average out to the zero vector each, $a, b$ are scalars, and $N, W$ are two independent vectors of i.i.d. normal RVs.

Now, $X$ and $Y$ are correlated, right?

 

[CaptainBlack]

Hello everyone!

I'm coming to notice day by day how our education is purely focused on memorizing and applying formulas rather than understanding the concept. Assume we have the following:

$X = aR + N$, and
$Y = bG + W$,

where $X, Y$ are random vectors, $R, G$ are strongly correlated random vector that average out to the zero vector each, $a, b$ are scalars, and $N, W$ are two independent vectors of i.i.d. normal RVs.

Now, $X$ and $Y$ are correlated, right?

I somehow suspect you have missed out some information, but under my interpretation of what you mean, yes.

If you write out what you mean by correlation it should be obvious what the answer is.

CB

PS My interpretation of what you mean when you ask are X and Y correlated is that you are asking: is \( E( (X-\overline{X}) (Y-\overline{Y})^t)\ne {\bf{0}} \)?

 

[OhMyMarkov]

Yes, this is what I mean. Wanted to make sure... I'll review the problem...