Consider a finite population U of size N = 5. We consider the following sample design:

s	{1, 2}	{3,4}	{3, 5}	{4, 5}	{2, 4}
p(s)	1/4	1/6	1/6	1/6	1/4

Table 1: The sample design

(i) Determine the first-order inclusion probabilities.

(ii) Determine the second-order inclusion probabilities.

(iii) Does this sample design correspond to simple random sampling without replacement? Systematic sampling? Bernoulli sampling? Justify your answers.

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

Course: MAT3777 University of ottawa