Difference between revisions of "Variance"
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(Created page with "==Definition== Given a random variable {{M|X}} we define the '''variance''' of {{M|X}} as follows: * <math>\text{Var}(X)=\mathbb{E}\left[(X-\mu)^2\right]</...") |
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:: But! <math>\mu=\mathbb{E}[X]</math> | :: But! <math>\mu=\mathbb{E}[X]</math> | ||
: <math>=\mathbb{E}\left[X^2\right]-2\mu^2+\mu^2</math> | : <math>=\mathbb{E}\left[X^2\right]-2\mu^2+\mu^2</math> | ||
| − | : <math>=\mathbb{E}\left[X^2\right]-\mu</math> | + | : <math>=\mathbb{E}\left[X^2\right]-\mu^2</math> |
| − | : <math>=\mathbb{E}\left[X^2\right]-\mathbb{E}[X]</math> | + | : <math>=\mathbb{E}\left[X^2\right]-(\mathbb{E}[X])^2</math> |
As required. | As required. | ||
Revision as of 23:57, 29 April 2015
Definition
Given a random variable X we define the variance of X as follows:
- Var(X)=E[(X−μ)2] where μ is the mean or expected value of X
Other forms
[Expand]
Theorem: Var(X)=E[X2]+(E[X])2
