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{{quote|… this advantage in the theory of chance is the product of the sum hoped for by the probability of obtaining it; it is the partial sum which ought to result when we do not wish to run the risks of the event in supposing that the division is made proportional to the probabilities. This division is the only equitable one when all strange circumstances are eliminated; because an equal degree of probability gives an equal right for the sum hoped for. We will call this advantage ''mathematical hope''.}}
The use of letter '''E''' to denote expected value goes back to [[William Allen Whitworth|W.A. Whitworth]] (1901) "Choice and chance". The symbol has become popular since for English writers it meant "Expectation", for Germans "Erwartungswert", and for French "Espérance mathématique".<ref>{{cite web|title=Earliest uses of symbols in probability and statistics|url=http://jeff560.tripod.com/stat.html}}</ref>
==Properties==
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