PAKISTAN JOURNAL OF STATISTICS, cilt.29, sa.3, ss.307-313, 2013 (SCI-Expanded)
The proofs of the central limit theorem are divided into two categories: elementary
and non-elementary. Proofs using the characteristic function are called non-elementary
while the other proofs are called elementary. Using differential equation, this paper gives
a new non-elementary proof for the central limit theorem. This proof is based on a
differential equation and does not use second order Taylor expansion of any characteristic function. It is apparent that given proof may only have a pedagogical importance.