Mixture of populations

A simple example simulating a mixture of two normal populations results in some important observations, nonnormality and nonsymmetry of the mixture conditional pdf, nonlinearity of the conditional mean as a function of the conditioning data, heteroscedasticity of the conditional variance and its nonmonotonicity as a function of distance of the unknown to the conditioning data. A comparison of the mixture statistics with those predicted by traditional models ignoring the mixture reveals the inadequacy and inappropriateness of these traditional approaches. A mixture of two multivariate normal populations is illustrated through the analytical expressions of its conditional distribution and moments.