See question attached - thank you for the help and i will give good feedback!

Problem 2. Let U1, .. . , U100 be independent uniform variables on [0, 1], and let S be the sum of the 20 largest numbers out of {U 1, . . . , U100}. Find the expectation and the variance of 8. (You may need results from Homework 1'7 in order to compute the numeric answer.) Please express your answers as a single simplied fraction, with the prime factorization of the denominator