$X_1,X_2....X_n$~Norm($\mu,\sigma^2$).What are the distributions of those random variable that is following:
1.$Y_1=\frac{X_1-X_2}{\sqrt{X_3^2+X_4^2}}$
2.$Y_2=\frac{\sqrt{n-1}X_1}{\sqrt{\sum_{i=2}^n X_i^2}}$
I think that both $Y_1$and $Y_2$ obey Student Distribution. But I can't prove my answers. Anybody help me? Thanks in advance!