 
Summary: An Asymptotic Expansion for the Inspection
Paradox
J.E. Angus
School of Mathematical Sciences
Claremont Graduate University
710 N. College Avenue
Claremont, CA 91711
December 14, 2004
Abstract
Suppose there are n families with children attending a certain school,
and that the number of children in these families are independent and
identically distributed random variables, each with probability mass func
tion PfX = jg = pj; j 1 with ...nite mean =
P
j 1 jpj: If a child is
selected at random from the school, and XI is the number of children in
the family to which the child belongs, it is known that limn!1 PfXI =
jg = jpj= ; j 1: Here, asymptotic expansions for PfXI = jg are devel
oped under the condition EjXj3
< 1:
