A note on the bivariate distribution representation of two perfectly   correlated random variables by Dirac's $\delta$-function
  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 
Andr\'es Alay\'on Glazunov and Jie Zhang
cs.NI