Mathematical statistics
Mathematical statistics uses probability theory and other branches of mathematics to study statistics from a purely mathematical standpoint. Thus, for example, a random sample is denoted by a sequence of random variables,
:
each following a certain probability distribution (usually they are considered independent and identically distributed).
The sample mean is expressed as a function of those variables,
:
and is therefore itself a random variable with a distribution. By proceeding in this fashion, mathematical statistics attempts to provide a theoretical basis for many practices in applied statistics.
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