Appropriate function for two Gaussians

Question

I'm searching for a $y(x)$ function that will produce normalized two Gaussians with a distance, something that looks like:

The picture is a bit-misleading, I need one that they do not cross each other at all.

Any ideas ?

Thank you !

Answer 1

Take something like $$f(x)=\frac1{\color{red}2\sqrt{2\pi}}\left(\exp\{-\frac{x^2}{2}\}\times I_{\{x\leq5\}}+\exp\{-\frac{(x-10)^2}{2}\}\times I_{\{x>5\}}\right)$$