Use Python to create a Monte Carlo approximation of the Beta distribution

The Monte Carlo approximation is a method used in statistics and mathematics to estimate numerical results using random sampling. This technique is especially useful for problems that are difficult or impossible to solve analytically.

The basic concepts of how the Monte Carlo approximation works are:-

1. Generate a large number of random samples from a probability distribution.
2. Perform calculations or simulations on these random samples.
3. Use the results of these simulations to estimate the desired quantity.

The steps involved in creating a Monte Carlo approximation are:-

1. Define the problem by identifying the problem or quantity to be estimated.
2. Use a random number generator to produce a large set of random variables from the appropriate distribution.
3. Compute the mean of the simulation results, which approximates the expected value or solution to the problem.

There are several reasons why analysts choose to use a Monte Carlo approximation, which are:-

1. They are flexible and can be used to solve a wide variety of problems across different fields, such as finance, engineering, physics, and healthcare.