To compute moments under the Fisher-Yates distribution (4.4), let ur =

u(u − 1)···(u − r + 1) r > 0 1 r = 0 be a falling factorial power, and let {li} be a collection of nonnegative integers indexed by the haplotypes i = (i1 ...,im). Setting l = 

i li and ljk = 

i 1{ij=k}li, show that E



i n

li i

=

m j=1



k(njk)

ljk

(nl)m−1 .

In particular, verify that E(ni) = n m j=1 njij n .