📘 Chapter 10: Random Numbers and Simulations in NumPy — Your Portal to Probability and Chaos

🎲 “Randomness isn’t chaos—it’s creativity waiting to be simulated.”

Welcome to the 10th and final chapter in this NumPy beginner-to-pro series!
Throughout our journey, you’ve explored arrays, reshaped them, filtered them with logic, and even sorted them like a boss.

Now, we dive into the world of randomness and probability simulations — one of the most exciting and widely used parts of NumPy, especially in:

• Machine learning

• Games

• Simulations

• Statistical modeling

• Data augmentation

Let’s explore the mighty np.random module — a complete toolbox to generate everything from random floats and integers to entire probability distributions.

🎯 What You’ll Learn:

• Generating random integers and floats

• Simulating coin flips, dice rolls, and games

• Creating arrays of random numbers

• Using probability distributions: normal, uniform, binomial

• Seeding for reproducibility

🎰 1. Generating Random Integers

import numpy as np

# Single random integer between 0 and 10 (excluding 10)
print(np.random.randint(0, 10))

🎲 Dice Roll Simulation:

# Simulate 5 dice rolls
dice_rolls = np.random.randint(1, 7, size=5)
print("Dice rolls:", dice_rolls)

Output example:

Dice rolls: [4 2 6 3 5]

🔢 2. Generating Random Floats

# Random float between 0 and 1
print(np.random.rand())

# Array of 3 random floats
print(np.random.rand(3))

🧊 Example: Simulate temperatures in Celsius

temps = 20 + 10 * np.random.rand(5)  # 20 to 30 degrees
print("Simulated temps:", temps)

📈 3. Random Sampling from Arrays

🔄 np.random.choice()

colors = ['red', 'green', 'blue']
chosen = np.random.choice(colors, size=5, replace=True)
print(chosen)

🪙 Simulate a Coin Toss

tosses = np.random.choice(['Heads', 'Tails'], size=10)
print(tosses)

🔁 4. Shuffling and Permutation

🔀 shuffle() — modifies the original array

arr = np.array([1, 2, 3, 4, 5])
np.random.shuffle(arr)
print(arr)

🔀 permutation() — returns a new shuffled copy

new_arr = np.random.permutation(arr)
print(new_arr)

📌 Great for data shuffling in ML training/testing splits.

🎯 5. Seeding the Random Generator

Want reproducibility in results (for debugging or sharing)?

🔢 np.random.seed()

np.random.seed(42)
print(np.random.randint(0, 10, size=5))

You’ll get the same result every time you run this code.

📊 6. Probability Distributions in NumPy

NumPy supports a variety of probability distributions, which are essential in simulations and statistical modeling.

📌 a. Uniform Distribution – Equal probability in range [low, high)

uniform = np.random.uniform(low=0, high=100, size=5)
print("Uniform distribution:", uniform)

📌 b. Normal (Gaussian) Distribution – Bell curve

normal = np.random.normal(loc=0, scale=1, size=5)
print("Normal distribution:", normal)

Perfect for simulating real-world measurements (e.g., heights, weights).

📌 c. Binomial Distribution – Discrete yes/no outcomes

binomial = np.random.binomial(n=10, p=0.5, size=5)
print("Binomial outcomes:", binomial)

🎲 7. Simulation Examples

🧪 Simulate 1000 Coin Tosses

tosses = np.random.choice(['H', 'T'], size=1000)
heads = np.count_nonzero(tosses == 'H')
tails = 1000 - heads
print(f"Heads: {heads}, Tails: {tails}")

🎲 Simulate 1000 Dice Rolls and Count 6s

rolls = np.random.randint(1, 7, 1000)
sixes = np.count_nonzero(rolls == 6)
print("Number of sixes rolled:", sixes)

🎯 Simulate Student Test Scores

# Mean = 75, Std Dev = 10
scores = np.random.normal(loc=75, scale=10, size=100)
print("Sample scores:\n", scores[:10])

🧠 8. Real-Life Applications

⚠️ Common Pitfalls to Avoid

📌 Summary Table

🔚 Wrapping Up Chapter 10

Congratulations — you’ve completed your NumPy beginner journey! 🎉

You now have the tools to:

• Simulate complex systems

• Generate synthetic data

• Work with probabilities and randomness

• Perform experiments, gaming logic, ML data shuffling, and more

With this final chapter, you’ve unlocked a full toolkit for numerical computing in Python — ready for use in everything from data science to simulations, from deep learning to decision-making models.

🧭 What’s Next?

Here are your next steps:

• Explore SciPy, Pandas, or Matplotlib to visualize and analyze your NumPy arrays.

• Use NumPy in projects: ML pipelines, statistical simulations, or even game dev.

• Revisit each chapter as your understanding deepens.