572 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 



which is ah-eady -written for the least favorable configuration. The tables^ 

 are not immediately applicable since the correlations 



piZ^Zi) = , J'*'^'^ , a ^ j) (A39) 



are not, in general, equal to ^. In the cases treated in Tables VI and VII, 

 p*2] ^ 0.5 and hence p^gii] < P[2]?[2] so that the correlations (A39) 

 are all less than |. It was found that linear interpolation on the required 

 value of n between the results for p = and p = ^ gives moderately 

 good results when n is large. The result for p = J is given by 



n - X ^P^fl^^ + ^:-y'^ (A40) 



with \ = 2B where B is given in Table V. The result for p = is given 

 by (A40) \vith X = Xo^ where Xo is the solution of the equation 



P{Z > -Xo} = P*"^'-'^ (A41) 



which can easily be found from univariate normal probability tables. 

 An explicit expression for the result of this linear interpolation is 



\ ^ Pu]g[ii(4i?-Xo-) +Pt2ig[2]Xo (^^^ ^* ^ ^ Q _) (^^^2) 



P 



^ CS / * * s 



iP[l] - P[2]) 



The expressions for the probability of a correct selection for the al- 

 ternative specification corresponding to (A36) and (A37) are 



cs 



T)^ n^ 



r F''~' {aw + h)fiw) dw (A43) 



= a(A; - 1) 1°° Tl - ^('^^^) F'-\w)f(w) dw (A44) 



„ = /^ > a,.d „ ^ ^"'-'-/"f^" a (A45) 



^ PmQvi] Vp[2]9[2] 



These expressions can also be e\'aluated by the method described by 

 Salzer, Zucker and Capuano. 



where 



