ON AN EXAMPLE OF SUMS OF PAIRWISE INDEPENDENT RANDOM VARIABLES FOR WHICH THE CENTRAL LIMIT THEOREM HOLDS

Let ＄￥{X_{n)}n￥geq 1￥}＄ be a sequence of symmetric pairwise independent and identically distributed (piid) random variables. If ＄EX_{1}=0,＄ ＄EX_{1}^{2}=1＄ , then the Central Limit Theorem (CLT) is proved by Dug Hun Hong [5]. In this paper we show that under the above assumptions the sequence so defined is a sequence of martingale differences and CLT follows from McLeish's result. The class of pairwise independent random variables for which CLT holds, described in [5], is in consequence the known class of martingale differences. Furthermore, the assumption of pairwise independency is not crucial there and may be weakened. It seems that the assumption of pairwise independency is not essential in CLT, but we give an interesting result in this direction. Furthermore, an example is provided to illustrate this result