# Thread: Discrete random variable, showing its a valid pdf

1. ## 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.

2. ## Re: Discrete random variable, showing its a valid pdf

Originally Posted by jackmorgan3
Here is a start; $\sum\limits_{x = 0}^\infty {\frac{{{\lambda ^x}}}{{x!}}} = ~?$

3. ## 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?