Let U1,...,U100 be independent uniform variables on [0,1], and let S be the sum of the 20 largest numbers out of {U1,...,U100}. Find the expectation and the variance of S. (You may need results from Homework 17 in order to compute the numeric answer.)Please express your answers as a single simplified fraction, with the prime factorization of the denominator.

The part "(You may need results from Homework 17 in order to compute the numeric answer.)" refers to the picture that I attached. This is the density function for the kth smallest number of the 100 uniform variables (U1...U100) where n below will be 100 since we have 100 variables.

(a) Plugging in f(u) = 1 and F(u) = u (for 0