Probability Mass function

[niranjan12345]

Hi,
I am trying to solve the below problem.


I am not able to figure out how to split or approach 1/x+1. I can sum the terms individually and apply the formula of e^x if its x+1. But here I am not able to do.
Any approaches would be helpful.
Regards
Niranjan

 

[tkhunny]

Hi,
I am trying to solve the below problem.
View attachment 13973

I am not able to figure out how to split or approach 1/x+1. I can sum the terms individually and apply the formula of e^x if its x+1. But here I am not able to do.
Any approaches would be helpful.
Regards
Niranjan

First, please note that "1/x+1" probably does not mean what you want. Use parentheses to clarify intent - or learn just a little LaTeX.

Second, can you demonstrate that [math]E[X] = \lambda[/math]?