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.
