Random Variable Moments

Results

If the integral of the $n$th power of a real-valued random variable exists, the $n$th moment of the random variable is the expectation of its $n$th power.

Notation

Let $(X, \mathcal{A} , \mathbfsf{P} )$ be a probability space. Let $x$ be a real-valued random variable on $X$ such that $\int x^n d\mathbfsf{P} $ exists. The $n$th moment of $f$ is $\E (f^n)$.