A. W. Marshall and I. Olkin [J. Am. Stat. Assoc. 62, 30–44 (1967; Zbl 0147.38106)] introduced a bivariate exponential distribution of \(X\) and \(Y\) which occurs in the context of a two-component system subject to shocks. In this paper, the authors obtain the probability density functions of \(X+Y\) and \(X/(X+Y)\), their \(n\)-th moments, and \(E(X^m Y^n)\).