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Math Help - Finding variance for a discrete random variable

  1. #1
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    Finding variance for a discrete random variable

    Let W be a discrete rv with pmf f(w) = c|w-4| for w within {0,1,...,8}.
    a) Find c.
    b) Find E(W).
    c) Find Var(W).
    d) Find Var((W-4)^2).


    I already found that c = 1/20, E(W) = 2.4, and Var(W) = 20.24; I'm just having problems with part (d). I split it up into:
    Var((W-4)^2) = E((W-4)^4) - (E((W-4)^2))^2

    I know that (W-4)^2 = W^2 - 8W + 16, but I can't really see how this would help. This there any way to go about this problem using the values that I have already found?
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  2. #2
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    Quote Originally Posted by uberbandgeek6 View Post
    Let W be a discrete rv with pmf f(w) = c|w-4| for w within {0,1,...,8}.
    a) Find c.
    b) Find E(W).
    c) Find Var(W).
    d) Find Var((W-4)^2).


    I already found that c = 1/20, E(W) = 2.4, and Var(W) = 20.24; I'm just having problems with part (d). I split it up into:
    Var((W-4)^2) = E((W-4)^4) - (E((W-4)^2))^2

    I know that (W-4)^2 = W^2 - 8W + 16, but I can't really see how this would help. This there any way to go about this problem using the values that I have already found?
    Var(W^2 - 8W + 16) = Var(W^2) + 8 Var(W) and you should know how to calculate Var(W^2) from the given pmf.
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    Would't you have to square the -8 when you take it out though? Should it be Var(W^2) + 64*Var(W)?
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  4. #4
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    Quote Originally Posted by uberbandgeek6 View Post
    Would't you have to square the -8 when you take it out though? Should it be Var(W^2) + 64*Var(W)?
    Yes. My mistake.
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