Sacara umum '''ekspektasi''' nyaeta tetempoan nu leuwih mungkin ngeunaan kajadian. Hasil nu kurang nguntungkeun ngakibatkeun naekna [[emotion]] '''kateupanujuan'''. Lamun sababaraha kajadian ngarupakeun hal nu teu sakabehna diperkirakeun disebutna [[surprise]]. Tempo oge [[anticipation]].
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Dina [[kamungkinan]] (hususna dina [[gambling]]), '''nilai ekspektasi''' (atawa '''ekspektasi''') oftina avariabel random variablengarupakeun isjumlah theprobabiliti sumunggal ofhasil thenu probabilitymungkin oftina eachsababaraha possiblepercobaan outcomeku of the experiment multiplied by its payoffhasilna ("valuenilai"). ThusMangka, itieu representsgmabaran therata-rata averagengeunaan amount onehiji "expectsekpektasi" tokeur winmeunang perunggal bettarohan iflamun betseta withtarohan identicalidentik oddsteu aresarua repeatedunggal manywaktu times''pengulangan''. NoteCatetan, thatnilai theeta valuesorangan itselfteu maybisa notdi-ekspektasi besacara expectedumum, in the general sense,saperti itteu maymirip beatawa unlikelykajadian ornu eventeu impossiblemungkin.
For exampleContona, an American [[Roulette]] wheelAmerika hasngabogaan 38 equallyhasil possible outcomeskamungkinan. ATarohan betdisimpen placeddina onhiji aangka single number paysbayaran 35-toka-1 (thisieu meanshartina thatyen hemanehna is paidmayar 35 times hiskali bettarohan, while also his bet is returned, together he gets 36 times his bet). So the expected value of the profit resulting from a $1 bet on a single number is, considering all 38 possible outcomes: ( -1 × 37/38 ) + ( 35 × 1/38 ), which is about -0.0526. Therefore one expects, on average, to lose over 5 cents for every dollar bet.
In general, if ''X'' is a [[random variable]] defined on a [[probability space]] (Ω, ''P''), then the '''expected value''' E''X'' of ''X'' is defined as
