Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'm using some Anki flash cards to study statistics and have come across an equation I don't recognize:

$$E(X)^2 = \sum r^2 P(X=r)$$

I found a similar equation in the last line of the proof of the Law of total expectation on Wikipedia.

I'm wondering if someone could point me to a place where this equation is described and possibly some applications for which it is used.

The Card deck is named Tyler GCE Maths S1 - Key facts and equations required for the OCR MEI Mathematics Statistics 1 exam.

share|improve this question
3  
your equation has a bit problem I guess. it should be $E[X^2]$ –  Seyhmus Güngören Aug 30 '12 at 20:56

1 Answer 1

up vote 1 down vote accepted

As Seyhmus mentioned, this should be $E[X^2] = \sum_r r^2 P(X=r)$. This is valid only for discrete random variables: the version for a continuous random variable with density $f(x)$ is $$E[X^2] = \int_{-\infty}^\infty r^2 f(r)\ dr$$ Both versions are a special case of the "Law of the Unconscious Statistician", which you can look up e.g. in Wikipedia.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.