Disclaimer - I'm not a statistician. Most of my knowledge on the subject is self-taught.
I'm trying to grasp how continuous random variables can be used in conjunction with a discrete Poisson process.
Say you measure rainfall data in your area for one year. You can determine the probability if it will rain tomorrow by applying a discrete Poisson distribution. However, let's say you want to take it a step further and predict whether it will rain tomorrow and how much it will rain based on gathered data.
If for every time it rained you measured the amount of rainfall, would determining the amount of rainfall given that it rains be considered a Poisson process? Or is it more along the lines of conditional probability alongside a discrete Poisson distribution?