A side from being a double integral or volume give two stati

A side from being a double integral or volume, give two statistical interpretations of integral_-infinity^infinity integral_infinity^infinity x f_x|y (x|y) f_y(y) dx dy justify them

Solution

The given double integral and the integral , with X, Y interchanged give formulae for the conditional expectations of E(X|Y) and E(Y|X)