Density of the first k coordinates of a uniform random variable
Suppose that X is distributed uniformly in the n-sphere . Then apparently the distribution of , the first coordinates of X has density with respect to Lebesgue measure in , moreover if , then it is proportional to
and otherwise is 0. I tried to compute this using the fact that , when are iid standard normal variables, but was unable to simplify the integrals. Does anyone know/can point me to a place where this density is derived?