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The mathematical expectation of a continuously distributed random variable $\text{[math]}$ with probability density function $\text{[math]}$ is

\text{[math]}

The expectation is also known as the mean of $\text{[math]}$ .

The expectation with respect to some function $\text{[math]}$ where $\text{[math]}$ is distributed according to $\text{[math]}$ is

\text{[math]}

For a discretely distributed random variable $\text{[math]}$ with probability mass function $\text{[math]}$ it is

\text{[math]}

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Expectation (math)