Question

What is the mathematical formula for the variance of a continuous random variable?

Answer 1

The formula is the same whether it is a discrete random variable or a continuous random variable.

Explanation:

irrespective of the type of random variable, the formula for variance is `sigma^2` = E(`X^2`) - `[E(X)]^2`.
However, if the random variable is discrete, we use the process of summation.

In the case of a continuous random variable, we use the integral.
E(`X^2`) = `int_-infty^infty x^2 f(x)dx`.
E(X) = `int_-infty^infty x f(x)dx`.
From this, we get `sigma^2` by substitution.