Functions of Two Random Variables: Jacobian Matrix Partial Derivatives

184 Views Asked by At

I currently have a joint distribution for random variable transformation problem and I do not know how to make the Jacobian Matrix.

So far the problem states that $f(x,y)=\frac{2x+y}{36}$ $0 \leq y \leq x$ and $x + 2y \leq 6$. Random variable $V = X * Y$.

So I started first by converting V to $Y = \frac{V}{X}$ and then rewriting the bounds in the same terms such as $0 \leq v \leq x^2$ and $v \leq \frac{x(6-x)}{2}$. However, from here I am stuck, since I do not know how to take the jacobian matrix. Which partial derivative goes to each corner and with respect to what variable do I take the partial?