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    Var(X+Y+Z)




    What is the formula for the variance of 3 dependent variables?

    For 2 dependent variables, the formula is

    Var(X)+Var(Y)+2*Cov(X,Y)

    What is Var(X+Y+Z) if the variables are dependent? Please do not give me the general formula for n number of variables. I've seen it but I don't understand it. If I see an example with 3 variables then I think I can figure it out. Thanks.
    Last edited by shrek; 07-08-2008 at 03:09 PM.

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    Quote Originally Posted by shrek View Post
    What is the formula for the variance of 3 dependent variables?

    For 2 dependent variables, the formula is

    Var(X)+Var(Y)+2*Cov(X,Y)

    What is Var(X+Y+Z) if the variables are dependent? Please go not give me the general formula for n number of variables. I've seen it but I don't understand it. If I see an example with 3 variables then I think I can figure it out. Thanks.

    How about:

    Var (X + Y + Z) = Var(X) + Var(Y) + Var(Z) + 2Cov(X,Y) + 2Cov(X,Z) + 2Cov(Y,Z).


    I can write out a short proof if you would like.

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    Quote Originally Posted by Dragan View Post
    How about:

    Var (X + Y + Z) = Var(X) + Var(Y) + Var(Z) + 2Cov(X,Y) + 2Cov(X,Z) + 2Cov(Y,Z).


    I can write out a short proof if you would like.
    thanks! no proof necessary. how about Var(X+Y-Z)? is this right?

    Var (X + Y - Z) = Var(X) + Var(Y) - Var(Z) + 2Cov(X,Y) - 2Cov(X,Z) - 2Cov(Y,Z)

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    Quote Originally Posted by shrek View Post
    thanks! no proof necessary. how about Var(X+Y-Z)? is this right?

    Var (X + Y - Z) = Var(X) + Var(Y) - Var(Z) + 2Cov(X,Y) - 2Cov(X,Z) - 2Cov(Y,Z)

    Well, you're always going to sum the variances so we have,


    Var (X + Y - Z) = Var(X) + Var(Y) + Var(Z) + 2Cov(X,Y) - 2Cov(X,Z) - 2Cov(Y,Z)

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    Re: Var(X+Y+Z)

    Quote Originally Posted by Dragan View Post
    How about:

    Var (X + Y + Z) = Var(X) + Var(Y) + Var(Z) + 2Cov(X,Y) + 2Cov(X,Z) + 2Cov(Y,Z).


    I can write out a short proof if you would like.
    Hi,
    Can you please write out the proof?

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    Re: Var(X+Y+Z)

    Var\left[\sum_{i=1}^n X_i\right]

    = Cov\left[\sum_{i=1}^n X_i, \sum_{j=1}^n X_j\right]

    = \sum_{i=1}^n \sum_{j=1}^n Cov[X_i, X_j]

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    Re: Var(X+Y+Z)


    hi can you help me with my statistics paper?

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