I am trying to solve the following question:
Suppose X ~ unif(B^n), B^n = {t in R^n | |t|<1} and let Yi = Xi ^2 where i = 1, ..., n
If i let U = X / ||X|| then what is the distribution of U1 ^2? and how can I find E(U) and Var(U)????
I thought I need to use the density of u1
f(u1) = [r(1/2 * n)] / [pi^(k/2) * r(1/2)(n-k)] * (1 - u1'u1)^(n-k)
where 0 < u1'u1<1
// r = gamma
I don't know what to do...T-T
Any help will be appreciated!!!