Hi group,

I have a (probably very simple) question that I could not think
through. i am hoping that you could please enlighten me a little bit.

Suppose I have two completely uncorrelated signals A and B. We can
assume that they take any form, say, continuous function or discrete
series. For convenience, let's assume they can be indexed. They have
the same length N. The question is, does this relationship hold?

<A> * <B> = <A * B>

Here <> represents mean, i.e. <A> = sum(A)/N.

I have done numerical experiments on this, and it appears that it
hods. I, however, could not come up with an analytical proof. Could
you please help me here?

A related question is that under what condition this relationship
breaks down. I know for sure that when A and B are related, the math
does not hold because <A>^2 != <A^2>. I think an analytical proof for
the previous question can help with this question as well, but I am
not sure.

Thanks a lot!

Regards,
Frank