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Math Help - Discrete random variable, showing its a valid pdf

  1. #1
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    Exclamation Discrete random variable, showing its a valid pdf

    Hi all,

    Stuck on this question that we're supposed to do over summer, hope someone can help.








    Discrete random variable, showing its a valid pdf-screen-shot-2012-08-11-01.22.26.png
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  2. #2
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    Re: Discrete random variable, showing its a valid pdf

    Quote Originally Posted by jackmorgan3 View Post
    Click image for larger version. 

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    Here is a start; \sum\limits_{x = 0}^\infty  {\frac{{{\lambda ^x}}}{{x!}}}  = ~?
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  3. #3
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    Re: Discrete random variable, showing its a valid pdf

    Please do not ask for additional in a PM. Post what you need to ask within the thread.
    \sum\limits_{x = 0}^\infty  {\frac{{{\lambda ^x}}}{{x!}}}  = e^{\lambda}

    Thus \sum\limits_{x = 0}^\infty  {{e^{ - \lambda }}\frac{{{\lambda ^x}}}{{x!}}}  = 1. Why and what does that tell you?
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