954 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 



equilibrium intervals (0, T). It has been convenient to display these in 

 three triangular arrays, the first consisting of expectations of products, 

 the second comprising the variances and covariances, and the third 

 exhibiting, for simplicity, the squared correlation coefficients, since the 

 correlation coefficients are never negative for these random variables. 



In Table III, the entry with coordinates (X, Y) is£'{A'F} foreciuilib- 

 rium (0, T). All three tables are expressed in terms of a, 6, T, h, r, and 

 C, the last of which is plotted in Fig. 2. 



The variances and covariances of the sufficient statistics are listed in 

 Table IV; the entries are of the form: 



cov {X, F} = E{XY\ - E{X\E{Y\. 



Table \', finally, lists the squared correlation coefficients; i.e., the 

 quantities 



cov' {X,Y} 



AX, Y) = 



var \X\ var {F} 



For any time interval (0, T), A has a Poisson distribution with param- 

 eter aT, so that Tdc does also. Therefore the distribution of dc is given 



by 



pr {(te 



< 



•r! = E 



n! 



where the summation is over ;/ < xT. Evidentlv 



