1. ## Basic Covariance Question

Hello,

I'm generally comfortable with the idea of covariance, but there's a way of writing covariance that i don't understand.

Could someone please explain how we get to the second way of writing covariance above?

I naively would have just multiplied what look like two binomials in the first expression, which of course would not produce the second expression.
Thanks for the help
Ben

2. Originally Posted by NYKarl
Hello,

I'm generally comfortable with the idea of covariance, but there's a way of writing covariance that i don't understand.

Could someone please explain how we get to the second way of writing covariance above?

I naively would have just multiplied what look like two binomials in the first expression, which of course would not produce the second expression.
Thanks for the help
Ben
You multiply out the brackets in the first form and replace terms like $\langle X \mu_Y\rangle$ by $\mu_X \mu_Y$ and knowing that $\langle \mu_X \mu_Y \rangle = \mu_X \mu_Y$.

RonL

3. I think your missing something in the equation or formula, it should be written as:
E { ( X - meanX) ( Y - meanY) }

E = Expected = the mean of some expression

so it's the mean value of the product (multiplication) of X minus its mean and Y minus its mean

so it can be expressed as the average value " E " of the multiplication of X minus its mean by Y minus its mean

and that's why when we convert it to real data, we take the sum of all (X-meanX)(Y-meanY) and divided it by N to average it

I think the expression on top is just a mathmatical way to express a mean value using " E "
but the technical form is the one ur familiar with