if we know E[X|a <= x<=b]=0 E[Y|c <= y<=d]=0 Z=X-Y Do we know if E[Z|-a-d<=z<=b-c]=0? Thanks a lot for help.
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Originally Posted by gracelhz if we know E[X|a <= x<=b]=0 E[Y|c <= y<=d]=0 Z=X-Y Do we know if E[Z|-a-d<=z<=b-c]=0? Thanks a lot for help. No because: let a=c=0, b=d=1 and: p(0 <= x<=1)=0 and p(c <= y<=d)=0 and: p(x=7)=1, p(y=6.5)=1. (and probability of any other result be 0) Then E[Z|-1<=z<=1]=0.5 .
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