I am aware there are similar questions about the subject, but my question is probably much more simple.
I want to know why is the expectation of the second moment of continuous time white-noise equal to the some constant times the delta function, or:
$E[w(t)w(t+\tau)] = Q \delta(\tau)$
I am aware of the difficulties involving the definition of a function that is discontinuous in all points, but I just wish to know why engineers defined it like this. I appreciate on-line references to the subject. Thank you.