Expected value

Definition

Given a random variable $X$ we define the expected value of $X$ as:

• $$\mathbb{E}[X]=\sum x\mathbb{P}[X=x]$$

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Addition of random variables

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Theorem:

$$\mathbb{E}[X+Y]=\mathbb{E}[X]+\mathbb{E}[Y]$$

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TODO: http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter6.pdf p7

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