In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.

### Variance definition

The variance of random variable X is the expected value of squares of difference of X and the expected value μ.

σ^{2} = *Var*(*X*) = *E*[(*X*^{ }– *μ*)^{2}]

From the definition of the variance we can get

σ^{2} = *Var*(*X*) = *E*(*X*^{ 2}) – *μ*^{2}

### Variance of continuous random variable

For continuous random variable with mean value μ and probability density function f(x):

or

### Variance of discrete random variable

For discrete random variable X with mean value μ and probability mass function P(x):

or

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### Properties of variance

When X and Y are independent random variables:

*Var*(*X+Y*) = *Var*(*X*) + *Var*(*Y*)

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