@wikipedia
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{\displaystyle \operatorname {E} [X]=\sum _{i=1}^{n}x_{i}\,p_{i}=x_{1}p_{1}+x_{2}p_{2}+\cdots +x_{n}p_{n}.} |
whereLet be a random variable with a finite number of finite outcomes | LaTeX Math Inline |
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| body | {\displaystyle x_{1},x_{2},\ldots ,x_{n}} |
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occurring with probabilities | LaTeX Math Inline |
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| body | {\displaystyle p_{1},p_{2},\ldots ,p_{n},} |
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respectively.
The expectation of is defined as
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Since all probabilities | LaTeX Math Inline |
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| body | {\displaystyle p_{i}} |
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add up to 1 (| LaTeX Math Inline |
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| body | {\displaystyle p_{1}+p_{2}+\cdots +p_{n}=1} |
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), the expected value is the weighted average, with | LaTeX Math Inline |
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| body | {\displaystyle p_{i}} |
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’s being the weights.
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