Suppose I have an $n$-dimensional unit-ball:
$$ \{(t_1,...,t_n) : t_1^2+...+t_n^2\le1\} $$
And suppose I have an $n$-dimensional random variable $(X_1,...,X_n)$ who distributes uniform in this unit-ball. How do I find the marginal expectation of $\mathbb E[X_i]$?
I know it's $0$, by "symmetry", but am looking for a more formal proof.