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A random sample can be thought of as a set of objects that are chosen randomly. More formally, it is "a sequence of independent, identically distributed (IID) random data points." In other words, the terms random sample and IID are synonymous. In statistics, "random sample" is the typical terminology, but in probability, it is more common to ...
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
Conceptually, simple random sampling is the simplest of the probability sampling techniques. It requires a complete sampling frame, which may not be available or feasible to construct for large populations. Even if a complete frame is available, more efficient approaches may be possible if other useful information is available about the units ...
Graphs of probability P of not observing independent events each of probability p after n Bernoulli trials vs np for various p.Three examples are shown: Blue curve: Throwing a 6-sided die 6 times gives a 33.5% chance that 6 (or any other given number) never turns up; it can be observed that as n increases, the probability of a 1/n-chance event never appearing after n tries rapidly converges to 0.
Note that not all finite exchangeable sequences are mixtures of i.i.d. To see this, consider sampling without replacement from a finite set until no elements are left. The resulting sequence is exchangeable, but not a mixture of i.i.d. Indeed, conditioned on all other elements in the sequence, the remaining element is known.
In the above example, not everybody has the same probability of selection; what makes it a probability sample is the fact that each person's probability is known. When every element in the population does have the same probability of selection, this is known as an 'equal probability of selection' (EPS) design. Such designs are also referred to ...
Nonprobability sampling is a form of sampling that does not utilise random sampling techniques where the probability of getting any particular sample may be calculated. Nonprobability samples are not intended to be used to infer from the sample to the general population in statistical terms.
In probability theory, a pairwise independent collection of random variables is a set of random variables any two of which are independent. [1] Any collection of mutually independent random variables is pairwise independent, but some pairwise independent collections are not mutually independent.