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

1 Answer
Nov 3, 2015

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.