The electron probability distribution function, $\rho$, defined as $$\rho (\mathbf{r})=n\int {\mathrm{\Psi }}^{\text{*}}[\mathbf{r}(1),\mathbf{r}(2)\text{...}\mathbf{r}(n)]\mathrm{\Psi }[\mathbf{r}(1),\mathbf{r}(2)\text{...}\mathbf{r}(n)]\text{d}\mathbf{r}(2)\text{...}\text{d}\mathbf{r}(n)$$ where $\mathrm{\Psi }$ is an electronic wave-function and integration is made over the coordinates of all but the first electron of $n$. The physical interpretation of the electron density function is that $\rho \mathrm{d}\mathbf{r}$ gives the probability of finding an electron in a volume element $\mathrm{d}\mathbf{r}$, i.e., electron density in this volume.