Alright, Ive asked many of my fellow students (who seem to be as lost as I am) and a few of my professors (none of whom really help in explaining it despite their good intentions), so hopefully you guys can help me

My professor said we're going to have to solve a problem that will take a Poisson distribution to Exponential. I understand that if you have a Poisson distribution where you only take 1 value, it can be simplified to . Similarly, the exponential equation is .

First, does this mean that ?

Second, he said that we were going to have to use integration to solve a problem. The example that he gave us where we'll have to take from poisson to exponential is for say 2<x<5. How would I do this through integration?