Moment of a Random Variable

Definition

The moment of a Random variable is the expected value of the Random variable raised to some power.

Raw Moment

$${\mathbb{M}}^k[X]=\mathbb{E}\left[X^k\right]$$

Central Moment

Is the moment of a Random variable that has been adjusted to be around the mean of mean of the distribution.

$${\tilde{\mathbb{M}}}^k[X]=\mathbb{E}\left[(X-\mathbb{E}[X]{)}^k\right]$$

Note:

• 1st Moment → Mean
• 2nd Moment → Variance
• 3rd Moment → Skewness