{\displaystyle f(x;\mu 1,\sigma _{1},\sigma _{2})={\frac {1}{\sigma _{1}{\sqrt {2\pi }}}}\,\exp \left(-{\frac {(x-\mu )^{2}}{2\sigma _{1}^{2}}}\right)-{\frac {1}{\sigma _{2}{\sqrt {2\pi }}}}\,\exp \left(-{\frac {(x-\mu )^{2}}{2\sigma _{2}^{2}}}\right).}