For any continuous random variable $X$, it is obvious that $|E X| \leq E|X|$.
My question is, what kind of distribution $P$, such that $X\sim P$ and satisfy $|E X| \geq c E|X|$ for some positive $c\in (0,1)$.
Asked
Active
Viewed 69 times
1
-
If $P(X\ge 0)=1$ or $P(X\le 0)=1$, and $0
cE[|X|]$ for all $c \in (0,1)$ – Henry Jul 06 '21 at 10:58 -
If $E[X]=0$ and $0
– Henry Jul 06 '21 at 10:59 -
That deals with positive random variables (and negative one) and those with zero expectation. I suspect all others where $0
$ and some larger $c$ where the inequality is $ – Henry Jul 06 '21 at 11:02