THE WEAK LAW OF LARGE NUMBER FOR NORMED WEIGHTED SUMS OF STOCHASTICALLY DOMINATED AND PAIRWISE NEGATIVELY QUADRANT DEPENDENT RANDOM VARIABLES

THE WEAK LAW OF LARGE NUMBER FOR NORMED WEIGHTED SUMS OF STOCHASTICALLY DOMINATED AND PAIRWISE NEGATIVELY QUADRANT DEPENDENT RANDOM VARIABLES

Let $\{X_n,\;n{\geq}1\}$ be a sequence of pairwise negative quadrant dependent (NQD) random variables which are stochastically dominated by X. Let $\{a_n,\;n{\geq}1\}$ and $\{b_n,\;n{\geq}1\}$ be sequences of constants such that $a_n>0$ and $0<b_n{\rightarrow}{\infty}$. In this note a weak law of large number of the form $({\sum}_{j=1}^na_jX_j-{\nu}_n)/b_n\rightarrow\limits^p0$ is established, where $\{{\nu}_n,\;n{\geq}1\}$ is a suitable sequence.

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