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Math Help - find E[(X-Y)^2] difficult to work out

  1. #1
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    find E[(X-Y)^2] difficult to work out

    if x,y are independent, identically distributed r.v.-s with mean u and variance sigma^2 , find E[(X-Y)^2].

    have tried but dont know how you could use x-y
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  2. #2
    Senior Member Dinkydoe's Avatar
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    E[(X-Y)^2]= E[X^2-2XY+Y^2]= E[X^2]-2E[XY]+E[Y^2]

    Now use that E[XY]=E[X]E[Y] ...since X,Y are independant.
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  3. #3
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    confused

    im a little confused..... i thought the question asked to find that formula using the fact mean is u and variance is sigma squared. Im probably wrong just dont know how to finish question ...thanks so much for taking time!!!
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  4. #4
    MHF Contributor harish21's Avatar
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    E(X) = \mu_{x}

    Var(X) = E[X^2] - (E[X])^2 = E[X^2] - \mu_{x}^2
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  5. #5
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    Ok trying figure this out I can't figure how you get to E(x-y)^2 I'm not sure am I just missing something simple or how you get it. Workin on it but getting no where. Is E(x-y)^2 a specific formula??
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  6. #6
    MHF Contributor harish21's Avatar
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    Look at post no. 2 by DinkyDoe. It has already been found out for you!
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  7. #7
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    He seemed to multiply out then simplify , do I use your info before this I'm failing to see the connection sorry thanks for helpin
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  8. #8
    MHF Contributor harish21's Avatar
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    Follow his instructions first, and then use my info!
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