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Math Help - Proving expected value of Poisson Distribution

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    Proving expected value of Poisson Distribution

    How can i prove that the expected value of a poisson distribution is lambda?

    Please help.
    Last edited by mr fantastic; July 2nd 2010 at 08:55 PM. Reason: Edited title.
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    Quote Originally Posted by ilikec View Post
    How can i prove that the expected value of a poisson distribution is lambda?

    Please help.
    From the definition: E(X) = \sum_{x=0}^{+\infty} x \cdot \frac{e^{-\lambda} \lambda^x}{x!} = \lambda e^{-\lambda} \sum_{x=1}^{+\infty}\frac{\lambda^{x-1}}{(x-1)!} = \lambda e^{-\lambda} \sum_{t=0}^{+\infty}\frac{\lambda^{t}}{t!} (the missing steps are left for you to fill in) and you should recognise what the sum is equal to ....

    Another way is to use the result found here: http://www.mathhelpforum.com/math-he...tribution.html

    Thread of related interest: http://www.mathhelpforum.com/math-he...sson-dist.html.
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