In this paper, we study the Hamming distance d(H)(X, Y) between two indepen
dent identical distributed (i.i.d.) random n-tuples X and Y over some finit
e set. Both lower and upper bounds are derived for the expectation Ed(H)(X,
Y) and the variance Dd(H)(X, Y). Also, a generalization of the Grey-Rankin
bound is given.