Switch

In a switch node, an input $k$ with $n$ discrete values selects one of the $n$ continuous valued inputs $s_{i}$ as the output: $s_{\mbox{out}} = s_{k}$. The required expectations are as follows:

$$\left< s_{\mbox{out}} \right> = \sum_{i=1}^{n} q(k=i) \left< s_{i} \right>$$ (13)

$$\left< s_{\mbox{out}}^{2} \right> = \sum_{i=1}^{n} q(k=i) \left< s_{i}^{2} \right>$$ (14)

$$\left< \exp s_{\mbox{out}} \right> = \sum_{i=1}^{n} q(k=i) \left< \exp s_{i} \right> .$$ (15)

The variance is obtained by $\mathrm{Var}\left\{s_{\mbox{out}}\right\} = \left< s_{\mbox{out}}^{2} \right> - \left< s_{\mbox{out}} \right>^2$ and $\left< s_i^2 \right> = \left< s_i \right>^2 + \mathrm{Var}\left\{s_i\right\}$.