International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 805-812
doi:10.1155/S0161171285000898
A note on convergence of weighted sums of random variables
Xiang Chen Wang1
and M. Bhaskara Rao2
1Department of Mathematics, Jilin University, Changchun, China
2Department of Probability \& Statistics, The University, Sheffield S3 7RH, UK
Abstract
Under uniform integrability condition, some Weak Laws of large numbers are established for weighted sums of random variables generalizing results of Rohatgi, Pruitt and Khintchine. Some Strong Laws of Large Numbers are proved for weighted sums of pairwise independent random variables generalizing results of Jamison, Orey and Pruitt and Etemadi.