Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the pdf x ranging from 0 to infinity.
a) Show that Z1=nY1, Z2 = (n-1)(Y2 - y1) Z3= (n-2)(Y3-Y2)... Zn = Yn - Y_(n-1) are independent and that each Z has the exp distribution.
b) Demonstrate that all linear functions of Y1, Y2,...,Yn such as can be expressed as a linear function of independent random variables.
so , , , etc...
So how would I find the jacobian?