For some time now I fight with an exercise I received. I have to calculate $\mathbb{E}[\vert\vert Z \vert\vert_2]$ and $Var[\vert\vert Z \vert\vert]$, that is the expected distance as well as variance from the point Z to the origin, within the d-dimensional unit ball $B_d(1)$ with radius 1. Here, Z is uniformely drawn from this unit ball.
Of course I know the definition of the expectation of a $\mathbb{R}^d$-valued random variable, i.e. $$(\mathbb{E}[Z])_i = \int_\mathbb{R^d} x_i\, p(x) dx $$
yet I have no idea how to calculate $\mathbb{E}[\vert\vert Z \vert\vert]$ or $Var[\vert\vert Z\vert\vert]$. What to do here?
EDIT: The answer is given as $\frac{d}{d+1}$. The actual task is to prove that this is the solution.