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Math Help - show that V(X) = lambda

  1. #1
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    show that V(X) = lambda

    I have a problem and I don't really want the solution just a push in the right direction.

    given that \Pr(X=r) = \frac{e^{\lambda}\cdot{\lambda ^{r}}}{r!} r = 0,1,.....

    show that Varience of X equals \lambda.

    It would be helpful if I had some definitions aswell.
    Last edited by mr fantastic; January 11th 2009 at 03:48 AM. Reason: Fixed the latex
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  2. #2
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    Hello,
    Quote Originally Posted by Animalxxv View Post
    I have a problem and I don't really want the solution just a push in the right direction.

    given that P(X=r) = \frac{e^{lambda}\cdot{lambda ^{r}}}{r!} r = 0,1,.....

    show that Varience of X equals lambda.

    It would be helpful if I had some definitions aswell.
    Note that \mathbb{E}(f(X))=\sum_{r=0}^\infty \mathbb{P}(X=r) f(r)
    where \mathbb{E} is the expectation.


    We know that the variance V is given by this formula :
    V(X)=\mathbb{E}(X^2)-\mathbb{E}(X)^2

    V(X)=\sum_{r=0}^\infty \mathbb{P}(X=r) r^2-\left(\sum_{r=0}^\infty \mathbb{P}(X=r)r\right)^2

    Can you do it ?



    Edit : there are other ways such as using generating functions. This was the most basic one that came in my mind ><
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  3. #3
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    Yep thank you very much for your help
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  4. #4
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    Quote Originally Posted by Animalxxv View Post
    I have a problem and I don't really want the solution just a push in the right direction.

    given that \Pr(X=r) = \frac{e^{\lambda}\cdot{\lambda ^{r}}}{r!} r = 0,1,.....

    show that Varience of X equals \lambda.

    It would be helpful if I had some definitions aswell.
    Read this thread: http://www.mathhelpforum.com/math-he...sson-dist.html
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