mixture of Gaussians, which is not itself Gaussian: $p(x_2) = \frac{1}{2}\text{N}(1,1) + \frac{1}{2}\text{N}(3,1),$ in which $\text{N}(\mu, \sigma^2)$ is the probability density of the Gaussian (aka normal ) distribution with mean $\mu$ and variance $\sigma^2$. The mean of the second dimension variable is $\text{E}(X_2) = \Pr(C_1)\text{E}(X_2|C_1) + \Pr(C_2) \text{E}(X_2|C_2)$ $\text{E}(X_2) = \frac{1}{2}