I'm currently doing my homework for my stats class and I have a question for one of my exercises:
Consider a population P of size N. We define a new sampling scheme in the following way: we first select a sample SA using a simple random sampling without replacement of size n1. Then, we sample SB in P outside of SA according to a simple random sampling without replacement of size n2. We obtain in a such a way the final sample S as S = SA ∪ SB.
Obtain the probability P(S = s) for a realization s (probability mass function). Is it equivalent to a simple random sampling with sample size n = n1 + n2?
My questions is:
I don't really understand the question and don't know what to answer. What kind of PDF am I supposed to describe? What does he mean by P(S=s) for some realization s?
In my understanding the question is asking what the probability is that the sample will contain a certain random variable. Can someone maybe give me a more concrete example so I can work it out?