On the number of positive sums of random variables

Abstract

1. The following theorem is due to P. Erdös and M. Kac ¹ P. Erdos and M. Kac, On the number of positive sums of independent random variables, Bull. Amer, Math. Soc., vol. 53 (1947), pp. 1011–20. View all notes : Let X ₁, X ₂, … be independent random variables each having mean 0 and variance 1 and such that the central limit theorem is applicable. Let S_k = X ₁ + ... + X _k and let N_n denote the number of S_k's 1 ≤ k ≤ n, which are positive. Then,