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sampling theorem is used to know about sample signal.
In the context of a sample of size n out of a population of N, any sample of size n has the same probability of being selected. This is equivalent to the statement that any member of the population has the same probability of being included in the sample.
The statement is false. For a fixed alpha, an increase in the sample size will cause a decrease in beta (but an increase in the power).
random sample is a big sample and convenience sample is small sample
A subset of sample space is taking a sample from that sample space.