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Math Help - independent random variables

  1. #1
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    independent random variables

    Can someone please help me with this question.


    independent random variables-untitled.jpg

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  2. #2
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    Quote Originally Posted by nerdo View Post
    Can someone please help me with this question.


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    (i) Well the joint density is the product of marginal densities, since they are independent. So can you do it now?

    (ii) Var(X-Y) = Var(X) + Var(-Y) = Var(X) + Var(Y) = 9 + 1 = 10

    The first equality is justified because X and Y are independent.
    Why is the second equality justified?

    (iii) E(X^2) = Var(X) + (E(X))^2 = 9 + 2^2 = 13

    (iv) E(X+Y) = E(X) + E(Y) = 2 - 3 = -1
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  3. #3
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    Unhappy

    I know this will sound stupid , but how do i calcaulate the joint density of product of marginal densities. I hav tried for hours but i can not seem to figure it out.
    Last edited by nerdo; January 26th 2009 at 10:54 AM.
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  4. #4
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    Quote Originally Posted by nerdo View Post
    I know this will sound stupid , but how do i calcaulate the joint density of product of marginal densities. I hav tried for hours but i can not seem to figure it out.
    I don't see the trouble here ....

    If X and Y are independent random variables and the pdf of X is f(x) and the pdf of Y is g(y) then the joint pdf of X and Y is given by f(x) g(y).
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