Hi guys, can help me to understand the notation we used to represent V "Explaining the formulas, Visualization, ...", I got the idea of Expectation Value E but, I did not get Conditional Variance. Thanks!
Conditional Variance For Discrete & Continous Random Variable X
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statistics
variance
1 Answers
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Are you familiar with the definition of variance? $$V(X) := E[(X-E[X])^2] = E[X^2] - E[X]^2.$$ It is the expected square distance of $X$ from its mean. The last expression $E[X^2] - E[X]^2$ is a common way to compute the variance.
Conditional variance extends this notion with conditioning on some event or random variable. Essentially, it is the same as variance, but conditioned on $A$. Note that the formula simply takes $E[X^2] - E[X]^2$ but replaces each expectation with the conditional expectation to get $E[X^2 \mid A] - E[X \mid A]^2$.
$$V(X \mid A) := E[(X-E[X])^2 \mid A] = E[X^2 \mid A] - E[X \mid A]^2.$$
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0Actually, I am not. Please, can you give me a link where it's explained well? Thanks. – 2017-01-05
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0@White159 Surely the source you are reading (from which you got your picture) explains it? – 2017-01-05
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0Unfortunately not, we have got very bad notes ..... I would appreciate it if you provide a link ... – 2017-01-05
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0@White159 http://www.math.uah.edu/stat/expect/Variance.html – 2017-01-05