202 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956 



also be expressed in the form 



^iKC^ZZt (-1) c.-. c, . 



plus another similar expression in which 6i , a are replaced by 62 , a~^ 

 respectively. For ^ > we need only add g to this result. This result 

 was used to compute E(T) in table lA f or a = 1 and a = 2. For a = oo 

 the expression simplifies to 



E{T) = e^rC: ± erl ^~^^'^\ (66) 



which can be shoAvn to be equivalent to 



E{T) = e,f: ^— (67) 



REFERENCES 



1. Bechhofer, R. E., Kiefer, J. and Sobel, M., On a Type of Sequential Multiple 



Decision Procedures for Certain Ranking and Identification Problems with 

 k Populations. To be published. 



2. Birnbaum, A., Statistical methods for Poisson processes and exponential 



populations, J. Am. Stat. Assoc, 49, pp. 254-266, 1954. 



3. Birnbaum, A., Some procedures for comparing Poisson processes or popula- 



tions, Biometrika, 40, pp. 447-49, 1953. 



4. Girshick, M. A., Contributions to the theory of sequential analj'sis I, Annals 



Math. Stat., 17, pp. 123-43, 1946. 



5. Wald, A., Sequential Analysis, John Wiley and Sons, New York, 1947. 



I 



