# Poisson distribution and random processes

## Main Question or Discussion Point

Hello!

I am writing because I recently became interested in probability distributions, and I have to you a few questions.

Poisson distribution is given as a probability:

$f(k;\lambda)=\frac{\lambda^{k}e^{-\lambda}}{k!}$

But what is lambda?

Suppose that we consider as an unrelated incident falling raindrops. If these drops fall 100 in 1 on a surface second how much $\lambda$ will be?

How to check if the falling drops of rain or some other unrelated events are described in this distribution?

Last edited:

From Wikipedia: λ is a positive real number, equal to the expected number of occurrences during the given interval. For instance, if the events occur on average 4 times per minute, and one is interested in the probability of an event occurring k times in a 10 minute interval, one would use a Poisson distribution as the model with λ = 10×4 = 40.

I'm not sure what you mean by "100 in 1."

Meant falling about 100 drops per second on the area.

Im curious how can be checked whether a process is described in this distribution.

For example, the number of drops falling on the glass. How can I check if they are described Poisson distribution.

I think you would also need a time, since λ measures the expected number of occurrences and not the rate.

I've only taken one statistics course, but generally the problem will explicitly tell you if it follows a Poisson distribution. There are tests for Poission distributions if you're doing "real world" statistics, but I don't know anything about such tests. Maybe try googling "Poisson distribution test."