I have a region $W$ with vertexes in $(0,0,0), (2,0,0), (0,3,0),(0,0,1)$ (a pyramid).
I have the random vector $(X,Y,Z)$ with the density $c$ if $(x,y,z) \in W$ and $0$ otherwise.
To find $c$ I do $$V = \int_{x=0}^{x=2} \int_{y=0}^{3-3x/2} \int_{z=0}^{z=1-x/2-y/3} dz \, dy \, dx,$$ and I get that $c=1$
What's $P\{\frac{1}{3} \leq Z \leq \frac{2}{3}\ | X= \frac{1}{4}, Y= \frac{1}$ ?