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Math Help - addition of expectation and variance

  1. #1
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    addition of expectation and variance

    Two variables X and Yare defined as normal random variables such that X-N(200,5^20) and Y-N(180,4^2). Find the expectation and variance for the variables A and B when. A=X+Y and B=X-Y
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  2. #2
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    Quote Originally Posted by pinkpoodle View Post
    Two variables X and Yare defined as normal random variables such that X-N(200,5^20) and Y-N(180,4^2). Find the expectation and variance for the variables A and B when. A=X+Y and B=X-Y
    The expectation operator is linear, so:

    E(\alpha X+\beta Y)=\alpha E(X)+ \beta E(Y)

    which gives the expectation of A and B straight off.

    Now there is an equivalent result for variances but here I will be more long winded:

    var(A)=E[(A-E(A))^2]=E(A^2) - (E(A))^2

    you know E(A) from the earlier part of this post, and:

    E(A^2)=E[(X+Y)^2]=E(X^2)+2E(XY) + E(Y^2)

    but as X and Y are independant E(XY)=E(X)E(Y), and of course:

    E(X^2)=var(X)+(E(X))^2

    and similarly for E(Y^2).

    CB
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  3. #3
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    sorry i do not understand would you beable to put in the values and the exact answers. many thanks
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  4. #4
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    Actually that was great help, I understand now.
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