RANDOM SAMPLE FROM AN INFINITE
UNIVERSE
It is relatively
difficult to explain the concept of random sample from
an infinite population. However, a few examples will show the basic
characteristic of such a sample. Suppose we consider the 20 throws of a fair
dice as a sample from the hypothetically infinite population which consists of
the results of all possible throws of the dice. If the probability of getting a
particular number, say 1, is the same for each throw and the 20 throws are all
independent, then we say that the sample is random. Similarly, it would be said
to be sampling from an infinite population if we
sample with replacement from a finite population and our sample would be considered as a random sample
if in each draw all elements of the population have the same probability of
being selected and successive draws happen to be independent. In brief, one can
say that the selection of each item
in a random sample from an infinite population is controlled by the same
probabilities and that successive selections are independent of one another.
Reference : C.R.Kothari
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