" aria-label="Anchor link to header"></a></h3>
<p>The absolute derivative of the inverse transform is</p>
<p><span class="math display">\[
\left| \,
\frac{d}{dy} \left( \exp(y) + a \right)
\, \right|
= \exp(y).
\]</span></p>
<p>Therefore, given the density <span class="math inline">\(p_X\)</span> of <span class="math inline">\(X\)</span>, the density of <span class="math inline">\(Y\)</span> is</p>
<p><span class="math display">\[
p_Y(y)
= p_X\!\left( \exp(y) + a \right) \cdot \exp(y).
\]</span></p>
</div>
