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Prove the computational formula for variance.

alexpercsi
alexpercsi asked
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Last Modified: 2012-05-06
Please prove that
V(Y) = E[Y*Y] - (E[Y]*E[Y]),

where V is the Variance and E is the Expected value of a random variable X
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Author

Commented:
Sorry, the random variable is Y, not X. I'm guessing you already picked up on that :)
Use that by defintion V(Y) = E( (Y-E(Y))^2 )
I thin the rest of that assignment should become clear then

Author

Commented:
I think I follow:

I have this result
V(Y)=E(Y^2)-E(2YE(Y))+E(Y)^2

Is it correct so far? If Yes, then can I continue like this?

V(Y)=E(Y^2)-2E(YE(Y))+E(Y)^2
V(Y)=E(Y^2)-2E(Y)E(Y)+E(Y)^2

Please excuse any idiotic statements, I am a beginner in probability theory, at the very most!
Yes, you can because E(cY) = cE(Y) and even though it depends on Y, E(Y) is just like any constant in this context

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Commented:
Thank You!
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