Tail integral formula for moments
= Tail integral formula for moments
For $q>0$ and a <random variable> $X$ with finite absolute $q$th moment, <Tonelli theorem> gives
$$
\mathbb E|X|^q=q\int_0^\infty t^{q-1}\mathbb P(|X|\geq t)\,dt.
$$
= Tail integral formula for moments
For $q>0$ and a <random variable> $X$ with finite absolute $q$th moment, <Tonelli theorem> gives
$$
\mathbb E|X|^q=q\int_0^\infty t^{q-1}\mathbb P(|X|\geq t)\,dt.
$$