Blackwell, David On an equation of Wald. (English) Zbl 0063.00422 Ann. Math. Stat. 17, 84-87 (1946). From the text: Let \(X_1, X_2,\dots\) be a sequence of independent chance variables with a common expected value \(a\), and let \(S_1, S_2, \dots\) be a sequence of mutually exclusive events, \(S_k\) depending only on \(X_1,\dots,X_k,\) such that \(\sum_{k=1}^\infty P(S_k)=1\). Define the chance variables \(n=n(X_1, X_2,\dots)=k\) when \(S_k\) occurs and \(W=X_1+\dots+X_n\). We consider conditions under which the equation \[ E(W)=aE(n),\tag{1} \] due to A. Wald [Ann. Math. Stat. 16, 117–186 (1945; Zbl 0060.30207), p. 142] holds. …More exactly, we investigate conditions on \(X_i\) under which (1) holds for every test \(n\) of finite expected value. Our results, Theorems 1 and 2, are that (1) holds if the \(X_i\) have identical distributions, or if they are uniformly bounded. Theorem 1 is a generalization of Wald [loc. cit.].(revised entry) Cited in 7 Documents MSC: 62L10 Sequential statistical analysis Citations:Zbl 0060.30207 PDFBibTeX XMLCite \textit{D. Blackwell}, Ann. Math. Stat. 17, 84--87 (1946; Zbl 0063.00422) Full Text: DOI Euclid