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

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

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Answer 1 · 2015-11-03T12:55:42

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 $σ^{2}$ $sigma^2$ = E( $X^{2}$ $X^2$ ) - ${[E (X)]}^{2}$ $[E(X)]^2$ .
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( $X^{2}$ $X^2$ ) = $\int_{- \infty}^{\infty} x^{2} f (x) d x$ $int_-infty^infty x^2 f(x)dx$ .
E(X) = $\int_{- \infty}^{\infty} x f (x) d x$ $int_-infty^infty x f(x)dx$ .
From this, we get $σ^{2}$ $sigma^2$ by substitution.

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

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