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Karten in diesem Stapel (4)
- 1Chapter 6 - Independent Distributions How are X and Y independent? Hint: px,y(x,y)Independent if px,y(x,y) can be a product of any function of X and any function of Y i.e. px,y(x,y) = g(X)h(Y)
- 2Chapter 6 - Expectation If X and Y are discrete and g(.) is a real valued function then E[G(X,Y)}=? Covariance of X and Y is? Correlation of X and Y is? What is Cov(X,X) equal to?SIGMAxSIGMAy[g(x,y)Pr(X=x,Y=y)]
Cov(X,Y) = E{[X-E(X)][Y-E(Y)]} = E(XY) - E(X)E(Y)
p=Corr(X,Y) = [Cov(X,Y)]/[sqrt(Var(X)Var(Y)]
Var(X) - 3Chapter 6 - Linear Combinations of Random Variables Var(aX+bY)=? Cov(aX+bY,cX+dY)=? Cov(X+Y,Z)=? Cov(SIGMAaiXi,SIGMAbjYj)=?a^2Var(X) +2abCov(X,Y) +b^2Var(Y)
acVar(X)+bdVar(Y)+(ad+bc)Cov(X,Y)
Cov(X,Z)+Cov(Y,Z)
SIGMAiSIGMAj[aibjCov(Xi,Yj) - 4Chapter 6 - Conditional Expectations E(X¦Y=Y)=? E(Y¦X=x)=? Ey[E(X¦Y)]=? Ex[E(Y¦X)]=? Proof of E(X)SIGMAx[xPr(X=x¦Y=y)]
SIGMAy[yPr(Y=y¦X=x)]
E(X)
E(Y)
Proof on separate sheet
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- Karteikarten am Ohne Titel, erstellt von Cara Wales am 27/01/2016.
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