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Homework Answers
E(Y|X=1)=1*(3/4)+(-1)*(1/4)=1/2
E(Y|X=-1)=(-1)*(3/4)+(1)*(1/2)=-1/2
E(Y)=E(Y|X=1)*P(X=1)+E(Y|X=-1)*P(X=-1)=(1/2)*(1/2)+(-1/2)*(1/2)=0
E(X)=xP(x)=1*(1/2)+(-1)*(1/2)=0
E(XY)=xyP(x,y)=1*1*(1/2)*(3/4)+1*(-1)*(1/2)*(1/4)+(-1)*(-1)*(1/2)*(3/4)+(-1)*(1)*(1/2)*(1/4)=0.5
therefore Cov(X,Y)=E(XY)-E(X)*E(Y)=0.5-0*0 =0.5
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