Suppose that the random variables X1,..., Xn are independent, and each random variable Xi has a continuous c.d.f. Fi. Also, let the random variable Y be defined by the relation
Y = −2∑(i=1~n) log Fi(Xi). Show that Y has the χ2 distribution with 2n degrees of freedom.
I don't see where this is heading. Is it possible to derive the χ2 distribution out of absolutely unknown CDFs?