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Math Help - Independent exponential R.V.

  1. #1
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    Unhappy Independent exponential R.V.

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    Last edited by Jason2009; May 7th 2009 at 01:51 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Jason2009 View Post
    Known a, b, c are 3 independent exponentials with E(a)=E(b)=E(c)=2.
    Find the variance of Y=a(b+c).

    Can someone please give me some hints?

    Thanks very much.
    The mean is:

    E(Y)=E(a(b+c))=\frac{1}{8}\int_0^{\infty}\int_0^{\  infty}\int_0^{\infty} a(b+c) e^{-a/2}e^{-b/2}e^{-c/2} ~da~db~dc

    which you should be able to do easily (using \overline{a}=\overline{b}=\overline{c}=2 )

    Then You will need:

    E(Y^2)=E([a(b+c)]^2)=\frac{1}{8}\int_0^{\infty}\int_0^{\infty}\int_  0^{\infty} [a(b+c)]^2 e^{-a/2}e^{-b/2}e^{-c/2} ~da~db~dc

    (use your knowlege of \text{var}(a) , \text{var}(b) and \text{var}(c) as an aide to evaluating this, you should not need to do any actual integrals that way)

    \text{var}(Y)=E(Y^2)-[E(Y)]^2

    CB
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  3. #3
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    Thanks ,CaptainBlack.
    What kind of the property did you use?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Jason2009 View Post
    Thanks ,CaptainBlack.
    What kind of the property did you use?
    If X, Y and Z are independedent RVs then their joint density:

     <br />
p(x,y,z)=p(z)p(y)p(z)<br />

    where p(x), p(y) and p(z) are the marginal densities of X, Y and Z respectivly.

    CB
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