Monte Carlo integration
Monte Carlo integration is like playing a game of guessing with lots of friends. Imagine you have a huge jar of M&Ms and you want to know how many there are inside. You invite a bunch of friends over and ask them to guess how many M&Ms are in the jar. You then take the average of all these guesses and use that as your estimation. The more friends you have, the better your estimation will be.
This is similar to Monte Carlo integration, which is a way to estimate some value using lot of random guesses. But instead of counting M&Ms in a jar, we use it to calculate things like the area under a curve or the average value of a function.
Let's say you want to find the area under a curve on a graph. You randomly select a bunch of points under the graph and count how many of them are under the curve. Then you divide that number by the total number of points and multiply it by the size of the box. This gives you an estimation of the area under the curve.
The more random points you select, the better your estimation will be. Just like how having more friends guess the number of M&Ms gives you a better estimation of the total number in the jar.
Overall, Monte Carlo integration is a way to estimate something using lots of random guesses. It's like playing a guessing game with your friends, but instead of M&Ms, you're trying to calculate things like the area under a curve or the average value of a function. The more random guesses you have, the better your estimation will be.
This is similar to Monte Carlo integration, which is a way to estimate some value using lot of random guesses. But instead of counting M&Ms in a jar, we use it to calculate things like the area under a curve or the average value of a function.
Let's say you want to find the area under a curve on a graph. You randomly select a bunch of points under the graph and count how many of them are under the curve. Then you divide that number by the total number of points and multiply it by the size of the box. This gives you an estimation of the area under the curve.
The more random points you select, the better your estimation will be. Just like how having more friends guess the number of M&Ms gives you a better estimation of the total number in the jar.
Overall, Monte Carlo integration is a way to estimate something using lots of random guesses. It's like playing a guessing game with your friends, but instead of M&Ms, you're trying to calculate things like the area under a curve or the average value of a function. The more random guesses you have, the better your estimation will be.