Hvilken regneformel finnes for kovarians?
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Cov(X,Y)=E[XY]−E[X]E[Y]\operatorname{Cov}(X,Y)=E[XY]-E[X]E[Y]Cov(X,Y)=E[XY]−E[X]E[Y], der E[XY]=∑x∑yxy p(x,y)E[XY]=\sum_x\sum_y xy\,p(x,y)E[XY]=∑x∑yxyp(x,y). Dette er ofte enklere enn definisjonen E[(X−μX)(Y−μY)]E[(X-\mu_X)(Y-\mu_Y)]E[(X−μX)(Y−μY)]. Merk spesialtilfellet Cov(X,X)=E[X2]−(E[X])2=Var(X)\operatorname{Cov}(X,X)=E[X^2]-(E[X])^2=\operatorname{Var}(X)Cov(X,X)=E[X2]−(E[X])2=Var(X).
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