Abstract
Given an
n-dimensional random variable
X
with a joint density
f
X
(x
1,…,x
n)
, the density of
Y
=h(
X
)
is computed as a surface integral of
f
X
in two cases: (a)
h linear, and (b)
h sum of squares. The integrals use the volume of the Jacobian matrix in a change-of-variables formula.