p; \approx &amp;
\frac{1}{M} \sum_{m = 1}^M
  \alpha^{(m)} + \beta^{(m)} \cdot \tilde{x}_n.
\end{eqnarray*}\]</span> This is possible because <span class="math display">\[
\tilde{y}_n^{(m)} \sim \textrm{normal}(\tilde{y}_n \mid \alpha^{(m)} +
\beta^{(m)} \cdot \tilde{x}_n, \sigma^{(m)}),
\]</span> and the normal distribution has symmetric error so that the expectation of <span class="math inline">\(\tilde{y}_n^{(m)}\)</span> is the same as <span class="math inline">\(\alpha^{(m)} + \beta^{(m)} \cdot
\tilde{