he CLT was introduced on
elementary level in the section (
Central
limit theorem
). The calculation of that section has restrictive
assumptions and the result lacks generality. Here we consider the issue with
greater precision.
Let
be a family of r.v. We assume that for each fixed
the family
is independent. This chapter studies limiting distributions of
as
.
We denote
and
the ch.f. and cumulative distribution functions of
respectively.
We think of sums
as quantities of similar magnitude even though the number of terms in these
sums increases. We formalize such view in the following definition.
