Difference between revisions of "Expected value"
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(Created page with "==Definition== Given a random variable {{M|X}} we define the '''expected value''' of {{M|X}} as: * <math>\mathbb{E}[X]=\sum x\mathbb{P}[X=x]</math> {{Todo...") |
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| + | ==Addition of random variables== | ||
| + | {{Begin Theorem}} | ||
| + | Theorem: <math>\mathbb{E}[X+Y]=\mathbb{E}[X]+\mathbb{E}[Y]</math> | ||
| + | {{Begin Proof}} | ||
| + | {{Todo|http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter6.pdf p7}} | ||
| + | {{End Proof}} | ||
| + | {{End Theorem}} | ||
{{Definition|Statistics}} | {{Definition|Statistics}} | ||
Latest revision as of 17:40, 8 May 2015
Definition
Given a random variable [ilmath]X[/ilmath] we define the expected value of [ilmath]X[/ilmath] as:
- [math]\mathbb{E}[X]=\sum x\mathbb{P}[X=x][/math]
TODO: Flesh page out
References
Addition of random variables
Theorem: [math]\mathbb{E}[X+Y]=\mathbb{E}[X]+\mathbb{E}[Y][/math]
