If I have a set of $n$ elements, and I want to assign to each-one some value $\phi$, drawn at random from a distribution $f(\phi)$ such that $\int_0^1f(\phi)\;d\phi\:=\:1$
Does this mean that the sum of the values of all my elements should be equal to one?
If not, what does it mean?
EDIT As I've learned from the below answers, the sum is not one. The integral is describing the probability density of $f(\phi)$.
Does anyone know how I would go about generating these $n$ values so it was like I picked them randomly from the above distribution?