For (Y1, Y2, Y3, Y4) ~ D4(1,2,3,4;5)
let Xk = [∑(from i=1 to k) Yi] / [∑(from i=1 to k+1) Yi] where k = 1,2,3
How can I prove X = (X1, X2, X3) is independent?
What I did was...
(Y1, Y2, Y3, Y4) ~ D4(1,2,3,4;5) = (Z1, Z2, Z3, Z4) / (Z1+Z2+Z3+Z4+Z5) where Z ~ N(0,1), Z IID G(1/2)
Now...