Bull. Korean Math. Soc. 2003; 40(2): 341-349
Printed June 1, 2003
Copyright © The Korean Mathematical Society.
Jong Il Baek, Han-Ying Liang, and Jeong Yeol Choi
Wonkwang University, Tongji University, Wonkwang University
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.
Keywords: negatively associated random variables, weak law of large numbers, weighted sum
MSC numbers: Primary 60F05; Secondary 62E10, 45E10
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