I'd like to show that if $\mathsf{E}(Z^4)=1$, then $\mathsf{E}(Z^3)\leqslant 1$.
I've been trying to use Jensen's inequality to show this, but haven't managed.
2026-04-12 01:39:26.1775957966
Bound on third moment
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$$|E[Z^3]|\leqslant E[|Z|^3]\leqslant E[Z^4]^{3/4}$$