Suppose x is an n -dimensional random variable with joint density f. If y = G (x), where G is a bijective, differentiable function, then y has density p Y : p Y ( y ) = f ( G − − 1 ( y ) ) | det [ d G − − 1 ( z ) d z | z = y ] | with the differential regarded as the Jacobian of the inverse of G (⋅), evaluated at y.