I am working though the exercises in the Computer Vision Models book.
Here I am at the Problem 2.7 which is described as:
The joint probability $\mathrm{Pr}(w, x, y, z)$ over four variables factorizes as
$\mathrm{Pr}(w, x, y, z) = \mathrm{Pr}(w)\mathrm{Pr}(z\mid y)\mathrm{Pr}(y\mid x,w)\mathrm{Pr}(x)$
Demonstrate that $x$ is independent of $w$ by showing that $\mathrm{Pr}(x,w) = \mathrm{Pr}(x)\mathrm{Pr}(w)$.
What I did in the given RHS was: $\mathrm{Pr}(w)\mathrm{Pr}(z,y\mid x,w)\mathrm{Pr}(x)$.
Is this right? I have a serious doubt about it, I have missed something big here. Just can't put my finger on it. And if this is wrong, any tips on how to proceed?