Write in the document the formula for calculating the variance of a random variable.

The variance of a random variable X is the mathematical expectation of the square of the deviation of X from its mean (mathematical expectation). The formula:

[ \mathrm{Var}(X) = \mathbb{E}[(X - \mathbb{E}[X])^2] ]

Expanding the brackets, it can be written as:

[ \mathrm{Var}(X) = \mathbb{E}[X^2] - (\mathbb{E}[X])^2 ]

Where:

• (\mathbb{E}[X]) — the mathematical expectation (mean) of the random variable X.
• (\mathbb{E}[X^2]) — the mathematical expectation of the square of X.

This shows how much the values of X are dispersed around the mean.