Inverse Transform</h3>
<p>The absolute derivative of the affine inverse transform is</p>
<p><span class="math display">\[
\left|
  \frac{d}{dy}
    \left(
      \frac{y-\mu}{\sigma}
    \right)
  \right|
= \frac{1}{\sigma}.
\]</span></p>
<p>Therefore, the density of the transformed variable <span class="math inline">\(Y\)</span> is</p>
<p><span class="math display">\[
p_Y(y)
=
 p_X \! \left( \frac{y-\mu}{\sigma} \right)
    \cdot \frac{1}{\sigma}.
\]</span></p>
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            </section>

        