The Absolute Difference Law For Expectations

We revisit the addition law for expectations and present a sibling law: the absolute law for expectations. We show that these two laws and their corresponding laws for probabilities can be reconciled under a single framework. As an application, we use the absolute law for expectations to calculate the mean absolute deviation. Finally, we remark on a hidden point in a related article previously published on these pages; this will help readers to avoid a potential pitfall.