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Math Help - Proving Convarience of a Dice Throw

  1. #1
    Super Member Deadstar's Avatar
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    Proving Convarience of a Dice Throw

    Ok...

    I have this question on a tutorial that i cant really figure out...

    A fair die is thrown twice, and let X and Y be the resulting numbers. Let U = X - Y and V = X + Y. Show that Cov(U,V) = 0. Are U and V independant?

    Now i know that if they are independant then this proves Cov(U,V) = 0 but i cant figure out if they are, and if they're not then ive no idea how to prove Cov(U,V) = 0.

    Can anyone help on this?

    Cheers
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Deadstar View Post
    Ok...

    I have this question on a tutorial that i cant really figure out...

    A fair die is thrown twice, and let X and Y be the resulting numbers. Let U = X - Y and V = X + Y. Show that Cov(U,V) = 0. Are U and V independant?

    Now i know that if they are independant then this proves Cov(U,V) = 0 but i cant figure out if they are, and if they're not then ive no idea how to prove Cov(U,V) = 0.

    Can anyone help on this?

    Cheers
    Cov(U,V) = E((U-\bar{U})(V-\bar{V}))=E((X-Y)(X+Y-7))

    .......... =E(X^2-Y^2-7X+7Y)=E(X^2)-E(Y^2)-7E(X)+7E(Y)

    but E(X^2)=E(Y^2),\ E(X)=E(Y), so:

    Cov(U,V)=0

    (and they are not independent)

    RonL
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