Controlled branching process
Okay, imagine you have a plant that starts as a seed. As you water it and give it sunlight, it grows bigger and bigger, and eventually it sprouts branches that also grow bigger and bigger.
Now imagine that sometimes, when a branch gets too big or too old, it splits into two smaller branches. And sometimes, instead of just one new branch growing from the old one, two or three or even more new branches sprout out.
A controlled branching process is kind of like that plant. But instead of a plant growing, it's a group of things that keep making more and more things based on certain rules.
Let's say you have a machine that makes little car parts, and you know that for every 100 car parts it makes, about 5 of them are defective and need to be remade. Now let's imagine that every time the machine makes a new car part, there's a chance it will create two more new car parts instead of just one.
You can use a controlled branching process to figure out how many good car parts you will have after a certain number of cycles. Each cycle is like a round of the game, where the machine makes a certain number of parts and some of them get remade, and some of them create more new parts.
By using certain math equations, you can predict how many good parts you'll end up with after a certain number of cycles. It's like guessing how many leaves a plant will have after a certain amount of time, based on how fast it's growing and how often it sprouts new branches.
Now imagine that sometimes, when a branch gets too big or too old, it splits into two smaller branches. And sometimes, instead of just one new branch growing from the old one, two or three or even more new branches sprout out.
A controlled branching process is kind of like that plant. But instead of a plant growing, it's a group of things that keep making more and more things based on certain rules.
Let's say you have a machine that makes little car parts, and you know that for every 100 car parts it makes, about 5 of them are defective and need to be remade. Now let's imagine that every time the machine makes a new car part, there's a chance it will create two more new car parts instead of just one.
You can use a controlled branching process to figure out how many good car parts you will have after a certain number of cycles. Each cycle is like a round of the game, where the machine makes a certain number of parts and some of them get remade, and some of them create more new parts.
By using certain math equations, you can predict how many good parts you'll end up with after a certain number of cycles. It's like guessing how many leaves a plant will have after a certain amount of time, based on how fast it's growing and how often it sprouts new branches.