The distribution of the product XY of random variables X and Y is of interest in many applied problems. The existing literature deals with cases when X and Y arise from the same family of distributions. In this paper, we study the distribution of XY

摘要

In this paper, we introduce the notions of pair-wise m-dependence and blockwise and pairwise m-dependence of random variables {Xn,n > 1}. For a sequence of blockwise and pairwise m-dependent random variables {Xn,n > 1}, we provide conditions for (∑from j=1 to n of (x_j - Ex_j))/(n~(1/r)) → 0 a.s. as n →　 ∞(1 ≤ r < 2). We also establish the strong law of large numbers for sequences of pairwise m-dependent random variables.