🎯 Simulating the Law of Large Numbers with R

This project demonstrates the Law of Large Numbers using the standard normal distribution in R.

I simulate random values and check what proportion of them fall between -1 and 1. According to the 68–95–99.7 rule, about 68.2% of values in a standard normal distribution should fall within this interval.

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📊 What This Project Does

• Generates N random values from the standard normal distribution
• Counts how many values lie between -1 and 1
• Calculates the proportion and compares it to the theoretical 68.2%
• Visualizes the distribution using:
  • Density plot with shaded region between -1 and 1
  • Histogram with highlighted range
  • Bar plot comparing theoretical and simulated values

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🧠 Why It Matters

This is a practical demonstration of how the Law of Large Numbers works:

The larger the sample size, the closer the result gets to the expected theoretical value.

It's also a great way to practice working with:

• Loops and conditionals in R
• Basic data visualization
• Statistical thinking using simulation

📸 Sample Output

You can expect an output like: Simulated Proportion: 0.6823 Which closely matches the theoretical value of 0.682.

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🚀 Run it Yourself

You can run the script using any R environment (e.g., RStudio). Feel free to modify the value of N to see how results vary with smaller or larger sample sizes.

👩‍💻 Author

Samira Sadeghi Data Science student in Milan 🇮🇹 Researcher in Machine Learning & Cancer Detection 💬 Passionate about R, Python, and building insight from data

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⭐️ If you like this project

Give it a ⭐️ on GitHub