| For N = 1, 2, ..., let SN be a simple random sample of size n = n N from a population AN of size N, where 0 ≤ n ≤ N. Then with fN = n/N, the sampling fraction, and 1A the inclusion indicator that A ∈ SN , for any H ⊂ AN of size k ≥ 0, the high order correlations Corrk= EA∈H&parl0; 1A-fN&parr0; depend only on k, and if the sampling fraction fN → f as N → infinity, we show in this thesis that Nk/2Corr&parl0;k&parr0;→ &sqbl0;f&parl0;f-1&parr0;&sqbr0;k/2 EZk, keven and N&parl0;k+1&parr0;/2Corr k→&sqbl0;f&parl0;f-1 &parr0;&sqbr0;k-1 /2&parl0;2f-1&parr0;13 &parl0;k-1&parr0;EZk+1, kodd where Z is a standard normal random variable. |
