The position for a particle is random, with uniform distribution on the sphere whose centre is the origin and radius is 7. Calculate the expected value of the particle's distance from the origin.
For the problem, uniform means:
$$\begin{cases}f(x,y,z) = \frac{1}{\pi}\ \text{when}\ \sqrt{x^2 + y^2 + z^2} \leq 7 \\ 0\ \text{otherwise}\end{cases}$$
How do I calculate the expected value?
