# ML: Monte Carlo Methods

## Introduction

Conducting physical experiments to validate probabilistic models is not always justified. A reasonable alternative is numerical experiments. Unfortunately, all programming languages use somewhat "biased" random number generators. However, in most cases, they are sufficient.

## Variance of event frequency

Let's verify the previously derived formula for the variance of the probability of an event, which is obtained from $N$ observations. To do this, we will conduct $N_{exp}$ numerical experiments, in each of which we will simulate the occurrence of some event $A$ $N$ times with probability $p_A$. We will compute the variance of the empirical probability based on these experiments. Below is the corresponding code.