Compound Poisson process

A compound Poisson process is a type of process where things happen randomly over time, and those things happen in groups. It's like when you go to the park and sometimes you see one bird, and sometimes you see a whole bunch of birds flying together. The Poisson part means that the groups happen randomly, like flipping a coin or rolling a dice.

For example, imagine you have a big jar of marbles, and every minute you reach in and take out a random number of marbles. Sometimes you might get one marble, sometimes five, sometimes ten. This is the Poisson part - the numbers of marbles you take out are random and don't depend on anything else.

But each time you take out marbles, you also get a certain amount of money depending on how many marbles you took out. Maybe every marble is worth 10 cents, so if you took out five marbles you'd get 50 cents. This is the compound part - the numbers of marbles you take out affects how much money you get.

So a compound Poisson process is just like that - random groups of things happening over time (Poisson), with each group affecting something else like how much money you make (compound).