Prove the computational formula for variance.

Posted on 2009-02-15
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
Question by:alexpercsi
    LVL 7

    Author Comment

    Sorry, the random variable is Y, not X. I'm guessing you already picked up on that :)
    LVL 20

    Expert Comment

    Use that by defintion V(Y) = E( (Y-E(Y))^2 )
    I thin the rest of that assignment should become clear then
    LVL 7

    Author Comment

    I think I follow:

    I have this result

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


    Please excuse any idiotic statements, I am a beginner in probability theory, at the very most!
    LVL 20

    Accepted Solution

    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
    LVL 7

    Author Closing Comment

    Thank You!

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