Let Y1<Y2<Y3<Y4<Y5 denote the order statistics of a random sample of size 5 from a distribution having pdf f(x) = e^(-x), 0<x<inf, zero else where. Show that Z1=Y2 and Z2=Y4-Y2 are independent.(Hint: find the joint pdf of Y2 and Y4)
I found the joint pdf g(Y2,Y4) and also joint pdf h(Z1,Z2)
Now how should I proceed this?