If the various x^ can be regarded as being independent (in the 

 probability sense), as we assume they are, then the variance of N^ can 

 be expressed as 



var(Nj^) " var(2xi) - ;^var(Xj_). (U) 



But var(xi) "^ (^)^ var(Hr) 



2 2 f 

 2. . dV . ii.2 2- . ,^. 



or s (xi) - -^ (— ) s (Hr) (5) 



Now, since s (T?j,) - — s (Hj.), (5) becomes 



R 



s2(xi) -0^ (£ii)2 s2(Hr) 

 d^ F^ 



and (U) gives us 



2,„ ^ R D^ ^/iiv2 r« 2 <SHj.)' 



(Nh) - RZi^^CpT^) ISHr 



R 



] (6) 



when we insert the well-known formula for the sample variance, s'^(Hj.). 

 In a similar manner, we find 



2,, . R D^ ^/^iiN2 r_^2 *^^r) . 



" (^^c) ■ Rii d^ SCjT-) Escr--Y-] 



It will be seen from the complete census worksheet that we have no 

 variable corresponding to the actual count of fishermen; the case is 

 simply that of tallying those that are seen. Consequently, we have 

 nothing to correspond to the variables Hj, and Cj., and it is therefore 

 impossible to construct a variance estimate for N^. 



Now although we have expressed all our estimates in terms of ^j_-^, 

 this is a number which v/e do not know. We must estimate f^j_ from kii, 

 which is our actual count. 



Consider Figure 12, which represents the fishing situation in L^ 

 during the census hour, that is, Lj^^. 



5-8 



