It’s worth highlighting that the two expectations do not condition on the same event. This explains why we can have E[A | all even] < E[B | even] even though A ≥ B almost surely: the two “all even”s actually refer to different events.
It’s worth highlighting that the two expectations do not condition on the same event. This explains why we can have E[A | all even] < E[B | even] even though A ≥ B almost surely: the two “all even”s actually refer to different events.