  In this paper we discuss the representation of the joint probability density
function of perfectly correlated continuous random variables, i.e., with
correlation coefficients $\rho=pm1$, by Dirac's $\delta$-function. We also show
how this representation allows to define Dirac's $\delta$-function as the ratio
between bivariate distributions and the marginal distribution in the limit
$\rho\rightarrow \pm1$, whenever this limit exists. We illustrate this with the
example of the bivariate Rice distribution
