This program uses a Monte Carlo simulation to estimate the value of Pi. The program generates random points within a square of side length 2, centered at the origin, and calculates how many of those points fall inside a unit circle. The ratio of the points inside the circle to the total number of points is used to estimate Pi.

How to Run

Make sure you have numpy and matplotlib installed, if not you can install them using the following command:
```
pip install requirements.txt
```
Save the script as pi.py.
Run the script using the command python pi.py or py pi.py if you have installed python from the microsoft store.

Output

The output is an animation of the Monte Carlo simulation and a GIF file named PI.gif saved in the same directory.

Portfolio Analysis with Real Stock Data

This program performs a Monte Carlo simulation to analyze the potential future returns of a portfolio composed of real stocks. Historical data is fetched from Yahoo Finance.

How to Run

Make sure you have numpy, pandas, matplotlib, and yfinance installed, just as before if dont have them installed you can install them with the following command:

pip install requirements.txt

Save the script as portfolio.py.
Run the script using the command python portfolio.py or py pi.py if you have installed python from the microsoft store.

Output

The output is a histogram of the simulated portfolio returns and summary statistics such as mean return, standard deviation, and Value at Risk (VaR).