Index: The Book of Statistical ProofsGeneral Theorems ▷ Probability theory ▷ Further moments ▷ Raw moment

Definition: Let $X$ be a random variable and let $n$ be a positive integer. Then, the $n$-th raw moment of $X$, also called ($n$-th) “crude moment”, is defined as the $n$-th moment of $X$ about the value 0:

\[\label{eq:mom-raw} \mu_n' = \mu_n(0) = \mathrm{E}[(X-0)^n] = \mathrm{E}[X^n] \; .\]

Metadata: ID: D97 | shortcut: mom-raw | author: JoramSoch | date: 2020-10-08, 03:31.