$X$ is a positive continuous random variable. $E[X^p]$ is the $p$-th moment of $X$, $p\ge2$. Is the following moment inequality valid? $E[X^p]\le (p-1)^{p/2}(E[X^2])^{p/2}$
If so, What is the name of this inequality, and how to prove it?
$X$ is a positive continuous random variable. $E[X^p]$ is the $p$-th moment of $X$, $p\ge2$. Is the following moment inequality valid? $E[X^p]\le (p-1)^{p/2}(E[X^2])^{p/2}$
If so, What is the name of this inequality, and how to prove it?
and that $P(X>y)dy/E(X)$ is a probability measure along with Jenson's Inequality.
– 2012-03-20consider the degenerate random variable $X\equiv 1$.
– 2012-03-20