Question: Let S be a sample selected by a Bernoulli design with probability . Let n s be the random size of S. Show that P

Let S be a sample selected by a Bernoulli design with probability . Let ns be the random size of S. Show that

P(S=sns=n0)=1/(n0N)

In other words, the conditional probability of S given ns is the same as the probability of a simple random sampling of fixed size n0 from N.

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

Course: MAT3777 (sampling) University of ottawa

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