Expected value

==Notations==
The use of the letter {{math|E}} to denote "expected value" goes back to [[William Allen Whitworth|W. A. Whitworth]] in 1901.<ref>Whitworth, W.A. (1901) ''Choice and Chance with One Thousand Exercises.'' Fifth edition. Deighton Bell, Cambridge. [Reprinted by Hafner Publishing Co., New York, 1959.]</ref> The symbol has since become popular for English writers. In German, {{math|E}} stands for ''Erwartungswert'', in Spanish for ''esperanza matemática'', and in French for ''espérance mathématique.''<ref>{{cite web|title=Earliest uses of symbols in probability and statistics|url=http://jeff560.tripod.com/stat.html}}</ref>

When "E" is used to denote "expected value", authors use a variety of stylizations: the expectation operator can be stylized as {{math|E}} (upright), {{mvar|E}} (italic), or <math>\mathbb{E}</math> (in [[blackboard bold]]), while a variety of bracket notations (such as {{math|E(''X'')}}, {{math|E[''X'']}}, and {{math|E''X''}}) are all used.

Another popular notation is {{math|μ<sub>''X''</sub>}}, whereas {{math|⟨''X''⟩}}, {{math|⟨''X''⟩<sub>av</sub>}}, and <math>\overline{X}</math> are commonly used in physics,{{sfnm|1a1=Feller|1y=1968|1p=221}} and {{math|M(''X'')}} in Russian-language literature.