# 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

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.