I'm asked to find the marginal distribution of $(X,Y)$ as $(X,Y,Z)$ is a point chosen uniformly on the unit sphere.
I've worked out that the joint density function $f_{XYZ}(x,y,z) = \frac{3}{4\pi}$ for $x^2+y^2+z^2 \leq 1.$
I know how to find the marginal distribution when dealing with 2-dimensions, but I'm not sure how I should set up the integrals in this case.
Would this be the correct way to go,
$$F_{X,Y}(x,y) = \int_{-\infty}^x \int_{-\infty}^y \int_{z} f_{XYZ}(x,y,z) dzdydx,$$
or am I really computing the marginal distribution of $F_X(x)$ if I do that?
Also, I'm having some problems understanding the difference between finding the density function and distribution function in cases like this. To me, it seems to be the same method for both functions?