# Proof: First raw moment is mean

**Index:**The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Further moments ▷ First raw moment is mean

**Theorem:** The first raw moment equals the mean, i.e.

**Proof:** The first raw moment of a random variable $X$ is defined as

which is equal to the expected value of $X$:

\[\label{eq:momraw-1st-qed} \mu_1' = \mathrm{E}\left[ X \right] = \mu \; .\]**∎**

**Sources:**

**Metadata:**ID: P171 | shortcut: momraw-1st | author: JoramSoch | date: 2020-10-08, 04:19.