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expectation algebra


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The mathematical rules that govern expectations. For random variables X, Y, Xj, with expected values E(X), E(Y), and E(Xj), and for any constants a, b, aj, the following formulae hold, without any assumptions of independence:

E(X+Y)=E(X)+E(Y),

E(XY)=E(X)−E(Y),

E(aX+b)=aE(X)+b,

E(aX+bY)=aE(X)+bE(Y),

. The following law also holds, provided X and Y are independent:

E(XY)=E(X)×E(Y).

Subjects: Probability and Statistics.


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