Sorry, I haven't touched math for some time. My math skill is very rusty. $X$ is a random variable. Can I ask when is the following equation true (or is it always true?). "Condition" here I am referring the things such as convexity, idk, do we need anything such as convexity in the random variable in order to make things true?
$$|EX| \leq E|X|$$
If this is true, how do I know the gap between the two? $$\text{gap}=E|X| - |EX|$$