Convergence of weighted sums of independent random variables
- 1 March 1971
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 69 (2) , 305-307
- https://doi.org/10.1017/s0305004100046685
Abstract
1. Introduction. Let {Xk: k ≥ 1} be a sequence of independent, but not necessarily identically distributed, random variables. Suppose that the random variables Xn are uniformly bounded by a random variable X in the sense that(1) P(|Xn| ≥x) ≤ P(|X| ≥ x)for all x > 0. Write qn(x) = P(|Xn| ≥ x) and q(x) = P(|X| ≥ x).Keywords
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