A weak law for weighted sums of array of row $NA$ random variables

Abstract

Let $\{ X_{n k}~ | 1 \leq k \le n, n \ge 1 \}$ be an array of random variables and $ \{ a_ {n }| n \ge 1 \}$ and $\{ b_n | n \ge 1 \}$ be a sequence of constants with $a_{n} > 0, ~ b_n >0, n \ge 1.$ In this paper, for array of row negatively associated$(NA)$ random variables, we establish a general weak law of large numbers $(WLLN)$ of the form $ \left( \sum_{k=1}^n a_k X_{nk} - \nu_{nk} \right) / b_{n}$ converges in probability to zero, as $n \rightarrow \infty,$ where $\{ \nu_{nk} | 1 \le k \le n, n \ge 1 \}$ is a suitable array of constants.