fShow the following properties for a fixed-size sampling design:

(i)jUij=(n1)i,for alliU;j=i

Hint: Use the fact thatjUZiZj=(n1)Zi.j=i

(ii)iUjUij=n(n1);j=i

(iii)jUij=0,for alliU,andiUij=0 for alljU,whereij=ijij

Reference: Sampling: Design and Analysis, 3rd Edition, by S.L. Lohr (2022).

Course: MAT3777 (Sampling) University of ottawa