# Probability – Try to understand Fisher's proof

To the $$i = 1, points, n$$, To let
$$begin {equation} R_i: = frac {X_i} {X_1 + dots + X_n}, end {equation}$$
where the $$X_i$$These are exponential standard random variables. To let
$$R _ *: = max_ {1 lei le n} R_i.$$
Fisher gave the formula
$$begin {equation} P (R _ * x) = sum_ {j = 1} ^ n (-1) ^ {j-1} binom nj (1-jx) _ + ^ {n-1} end {equation}$$
to the $$x in (0,1)$$ (with some other notation) where $$u _ +: = max (0, u)$$, I have proof of this result and a certain generalization of it.

My problem is that I understand almost nothing in Fischer's proof (on pages 57-58 of his paper). In particular, I do not understand the following:

1. What does (the polynomial (?)) Mean $$f$$ in the $$t$$ (Introduced (?) On page 57 of Fisher's Paper) deals with the spline (?). $$text {P}$$ in the $$g$$;
2. Why does $$f$$ have to have different properties in a neighborhood of $$t = 1$$ Fisher says that $$f$$ must have?
3. How does Fisher leap from these properties? $$f$$ to the (correct) final expression for $$text {P}$$? Fisher seems to give absolutely no information.

I will be glad to receive any help to fill these gaps in my understanding.