Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the pdf $\displaystyle f(x) = e^{-x}$ x ranging from 0 to infinity.

Demonstrate that all linear functions of Y1, Y2,...,Yn such as $\displaystyle \Sigma a_i Y_i$ can be expressed as a linear function of independent random variables.

so:

$\displaystyle \Sigma a_i Y_i = a_1Y_1 + a_2Y_2 + ... + a_nY_n = a_1e^{-x_1} + a_2e^{-x_2} +...+a_ne^{-x_n} $

That can't be right though....