Let XXX be a random variable. Is it always true that E[∣X∣]≥∣E[X]∣E[|X|] \ge |E[X]|E[∣X∣]≥∣E[X]∣?
Only when E[X]=0E[X]=0E[X]=0
Yes, by triangle inequality
No, they are equal only when X≥0X \ge 0X≥0
No counterexample exists