We have for two random variables X and Y (one sum runs over j and one over k):(adsbygoogle = window.adsbygoogle || []).push({});

E(X+Y) = ƩƩ(x_{j+yk)P(X=xk,Y=yk) = ƩƩxjP(X=xk,Y=yk) + ƩƩykP(X=xk,Y=yk) Now this can be simplified to obtain E(X+Y)=E(X)+E(Y) if we use that: P(X=xk,Y=yk) = P(X=xk)P(Y=yk), because then (and same goes the other way around): ƩjP(Y=yk)P(X=xj)= P(Y=yk) But all this requires X and Y to be uncorrelated. Does the derivation above also hold if generally: P(xj,yk)=P(xj l Y=yk)P(Y=yk)?}

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# Expectation value of sum

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