">\(\textbf{y}\sim N(\textbf{X}\beta, \sigma^2\textbf{I})\)</span>. Find the relationship between the regularization parameter <span class="arithmatex">\(\lambda\)</span> in the ridge formula, and the variances <span class="arithmatex">\(\tau\)</span> and <span class="arithmatex">\(\sigma^2\)</span>.</p>
</details>
<details class="done"><summary>Soln. 3.6</summary><p>By Bayes' theorem we have </p>
<div class="arithmatex">\[\begin{eqnarray}
    P(\beta|\textbf{y}) &amp;=&amp; \frac{P(\textbf{y}|\beta)P(\beta