I am not sure that I understand when to use Normal Distribution and when to use Poisson distribution! For example, in RF communication the channel noise is mainly modeled as Normal Gaussian distribution, but why? And why not Poisson Distribution? And vice versa, why photon collection on a sensor (shot noise) is modeled as Poisson distribution?
In other words, why receiving data over RF follows a Gaussian noise model, but receiving data over Light follows a Poisson noise model?
First of all, Poisson distribution is a discrete distribution while Gaussian is continuous, so you can't really model a continuous noise using Poisson distribution and vice versa.
The reason noise is usually modeled as a Gaussian random variable is largely due to Central Limit Theorem; since noise is typically result of many different effects acting on the system, the noise can be astoundingly reliably modeled as a Gaussian.
The reason Poisson dist. is commonly used for number of occurrences is due to the fact that Poisson distribution is the number of occurrences of an exponentially distributed random variable, which in turn is a good model for an event occurence because exponential random variable has no memory and thus can be used to model events that may occur any time independent of the time passed without the event occuring.
