Averages and moments

This fourth paragraph examines the fundamental properties of random variables, which are grouped together under the general heading of "averages and moments". Unlike arithmetic averages, which can be used to calculate moments, the rigorous determination of these parameters requires the evaluation of the mathematical expectation.

Mathematical expectation requires prior knowledge of the theoretical probabilities P _j attached to discrete variables, or for continuous variables, access to the analytic forms of the probability density p (x).

Symbol conventions are used to distinguish between mean and expectation operators. In articles [R 210v2] and