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Math Help - Difficult problem

  1. #1
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    Difficult problem

    2. Let X1 and X2 be independent random variables, with means μ1 and μ2 and variances σ1^2 and σ2^2, respectively. Find the Covariance of Y1 = X1 and Y2 = X1 X2.

    So for this one is the covariance of y 1 just the standard formula of covariance without any manipulation? And how about y2?
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  2. #2
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    Quote Originally Posted by wolverine21 View Post
    2. Let X1 and X2 be independent random variables, with means μ1 and μ2 and variances σ1^2 and σ2^2, respectively. Find the Covariance of Y1 = X1[snip]
    Cov(X1, X1) = Var(X1)
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  3. #3
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    Quote Originally Posted by wolverine21 View Post
    2. Let X1 and X2 be independent random variables, with means μ1 and μ2 and variances σ1^2 and σ2^2, respectively. Find the Covariance of Y1 = X1 and Y2 = X1 – X2.

    So for this one is the covariance of y 1 just the standard formula of covariance without any manipulation? And how about y2?
    Because X_1 and X_2 their joint pdf is the product of their individial pdf's.

    E( (Y_1-\bar{Y_1})(Y_2-\bar{Y_2})=\iint (x_1-\bar{x_1})(x_1-x_2-\bar{x_1}+\bar{x_2}) p(x_1)p(x_2) dx_1 dx_2

    Which you should be able to complete

    CB
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  4. #4
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    Quote Originally Posted by mr fantastic View Post
    Cov(X1, X1) = Var(X1)
    Your snip is in the wrong place, the covariance of Y_1 and Y_2 is required.

    CB
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  5. #5
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    Quote Originally Posted by CaptainBlack View Post
    Your snip is in the wrong place, the covariance of Y_1 and Y_2 is required.

    CB
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    Quote Originally Posted by CaptainBlack View Post
    Because X_1 and X_2 their joint pdf is the product of their individial pdf's.

    E( (Y_1-\bar{Y_1})(Y_2-\bar{Y_2})=\iint (x_1-\bar{x_1})(x_1-x_2-\bar{x_1}+\bar{x_2}) p(x_1)p(x_2) dx_1 dx_2

    Which you should be able to complete

    CB

    Wait so is this joint pdf I find the final answer?
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  7. #7
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    Quote Originally Posted by wolverine21 View Post
    Wait so is this joint pdf I find the final answer?
    No, you need to complete the double integral, you don't have to know the actual pdf's for X_1 and X_1 it is sufficient to know their means and variances and that they are independant (so Cov(X_1,X_2)=0 amoung other things).

    CB
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