what could be the meaning of last term in the correlation equation?

[Ranjini]

E= sqrt(<x^2><y^2>-(<x*y>)^2).
In this equation what exactly <x*y>^2 represents? pls help

[Dragan]

E= sqrt(<x^2><y^2>-(<x*y>)^2).
In this equation what exactly <x*y>^2 represents? pls help

What you have written is not the equation for the product-moment coefficient of correlation. And, why do you use the
notation "< >"?

[BGM]

The notation < > usually mean inner product of a Hilbert space, which can be defined as the covariance between two random variables. However it has two arguments :P

[Dragan]

A think a more commonly used notation (for the product moment correlation) is :

\cos \left ( \theta \right )=\frac{X\cdot Y}{\left \| X \right \|\left \| Y \right \|}

where the numerator is the dot product.