Discrete random variable, showing its a valid pdf

**jackmorgan3** · August 10th 2012, 04:23 PM

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

**Plato** · August 10th 2012, 04:42 PM

Originally Posted by jackmorgan3

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Here is a start; $\sum\limits_{x = 0}^\infty {\frac{{{\lambda ^x}}}{{x!}}} = ~?$

**Plato** · August 11th 2012, 05:03 AM

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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