# What does the angle bracket mean in variance formula?

When I check the formula of variance in Mathworld which is

$$\sigma^2 \equiv \langle\ (X - \mu)^2 \rangle\$$

Though I'm more familiar with the other formula, I just wanted to know what does the angle bracket mean aside from the formula in variance.

• math world defines it: and <X> denotes the expectation value of X. Commented Jan 14, 2019 at 10:00
• see mathworld.wolfram.com/AngleBracket.html - the last sentence of the article proper. Commented Jan 14, 2019 at 13:04
• It means a physicist (or possibly a pure mathematician) is writing about probability :-).
– whuber
Commented Jan 14, 2019 at 15:44

It's the expected value of $$(X-\mu)^2$$, i.e., it's the same as $$\sigma^2=E[(X-\mu)^2]$$.
It means an inner product for the multi-dimensional case. When $$X \in \mathbb{R}^n$$ and $$n \geq 2$$ and want to define variance, the definition of the variance is related to the inner product of $$X-\mu$$ to itself, and denoted as $$\langle X-\mu, X-\mu\rangle$$