X is a differentiable distribution funciton with pdf $\displaystyle f_X$

g is continuously differentiable and one-one. let Y = g(x).

$\displaystyle f_Y (y) = f_X (h(y)) |det (\partial h / \partial y)|$

where $\displaystyle \partial h / \partial y$ is the Jacobian matrix $\displaystyle (\partial h_i / \partial y_i)_{1\leq i,j \leq k}$

can somebody explain this with a concrete example??

and what is the meaning of multiplying a Jacobian determinant??

thanks a lot