A WEAK LAW FOR WEIGHTED SUMS OF ARRAY OF ROW NA RANDOM VARIABLES
A WEAK LAW FOR WEIGHTED SUMS OF ARRAY OF ROW NA RANDOM VARIABLES
Let {<TEX>$x_{nk}\;<TEX>$\mid$</TEX>1\;\leq\;k\;\leq\;n,\;n\;\geq\;1$</TEX>} be an array of random varianbles and <TEX>$\{a_n<TEX>$\mid$</TEX>n\;\geq\;1\}\;and\;\{b_n<TEX>$\mid$</TEX>n\;\geq\;1} be a sequence of constants with <TEX>$a_n\;>\;0,\;b_n\;>\;0,\;n\;\geq\;1. In this paper, for array of row negatively associated(NA) random variables, we establish a general weak law of large numbers (WLLA) of the form (<TEX>${\sum_{\kappa=1}}^n\;a_{\kappa}X_{n\kappa}\;-\;\nu_{n\kappa})\;/b_n$</TEX> converges in probability to zero, as <TEX>$n\;\rightarrow\;\infty$</TEX>, where …