This simulation helps to visualize posterior probability distributions that are proportional to the product of a Gaussian PDF and CDF:

<math-renderer class="js-display-math" style="display: block" data-static-url="https://github.githubassets.com/static" data-run-id="dbc0421c8b9986410ee587bd77ac0310">$$p\left( x \right) \propto \sigma_1^{-1} \ \varphi\left( \frac{x - \mu_1}{\sigma_1} \right) \ \Phi \left( \frac{x - \mu_2}{\sigma_2} \right)$$</math-renderer>

We approximate the mean and variance by performing Newton's method once from both means, picking whichever evaluates to larger posterior density.