# change of variable

• Oct 24th 2008, 06:37 AM
graticcio
change of variable
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
• Oct 25th 2008, 01:26 AM
mr fantastic
Quote:

Originally Posted by graticcio
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