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A random sample is a random variable whose values are the samples:

A random sample can also be defined as a discrete random vector composed of non‐negative integer variables . The variable represents the number of times unit is selected in the sample. If the sample is without replacement then variable can only take the values 0 or 1 and therefore has a Bernoulli distribution. In general, random variables are not independent except in very special cases. The use of indicator variables was introduced by Cornfield (1944) and greatly simplified the notation in survey sampling theory because it allows us to clearly separate the values of the variables or from the source of randomness .

Often, we try to select the sample as randomly as possible. The usual measure of randomness of a probability distribution is the entropy.