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Math Help - Probability problem

  1. #1
    Newbie
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    Probability problem

    Hey !
    I have this exercise to do :
    Let Z be a standard normal random variable and let Y1=Z and Y2=Z^2.

    a) What are E(Y1) and E(Y2)?

    b) What is E(Y1Y2)?

    c) What is Cov(Y1, Y2)?

    d) Notice that P(Y2>1|Y1>1)=1. Are Y1 and Y2 independent?

    I found E(Y1)=0 and E(Y2)=1/2
    But then because it is not given that Y1 and Y2 are independent I can't find E(Y1Y2)

    Thanks for any help..
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  2. #2
    MHF Contributor
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    E[Z] - You're kidding, right? Maybe zero (0)?

    E[Z^2] - (E[Z])^2 = Var(Z)

    Consider E((Y1+Y2)^2)
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  3. #3
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    I'm asking for E(Y1Y2)...
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  4. #4
    MHF Contributor matheagle's Avatar
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    E(Y_1Y_2)=E(Z^3)=0 by symmetry
    Last edited by matheagle; February 3rd 2010 at 03:58 PM.
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