  If X and Y are real valued random variables such that the first moments of X,
Y, and XY exist and the conditional expectation of Y given X is an affine
function of X, then the intercept and slope of the conditional expectation
equal the intercept and slope of the least squares linear regression function,
even though Y may not have a finite second moment. As a consequence, the affine
in X form of the conditional expectation and zero covariance imply mean
independence.
