The expectation of the maximum of RVs is greater or equal to the maximum of the expectations

For any sequence of RVs X1,...,Xn the following holds: E[max{X1, ..., Xn}] >= max{E[X1], ..., E[Xn]}    (*) Proof. We have that max{X1, ..., Xn} >= Xi for all i. Thus, this holds in expectation as well, i.e. E[max{X1, ..., Xn}] >= E[Xi] for all i. Since this holds for all i, it holds for … Continue reading The expectation of the maximum of RVs is greater or equal to the maximum of the expectations