pr.probability - Is there any random variable which has unbounded fourth moment?

More generally, given $p > 1$, take any bounded function on $mathbb{R}$ which behaves like $1/|x|^p$ as $xto infty$, for example $1/(1+|x|^p)$. After renormalizing, this is will be the density of a random variable which has finite absolute $q$th moments for $0 le q < p-1$, and infinite $q$th moments for $q ge p-1$.

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