🎲 NumPy Random Number Generation

The Magic Dice Factory

Imagine you have a magical dice factory. Every time you press a button, it creates dice that roll to whatever numbers you need. Sometimes you want random numbers between 1 and 6. Sometimes between 1 and 1000. This factory can make dice for ANY numbers you want!

NumPy’s random module is exactly like this magical dice factory.

🎰 Random Number Generators

What is a Random Number Generator?

Think of a Random Number Generator (RNG) like a machine that picks lottery numbers. Every time you ask, it gives you a new surprise number!

import numpy as np

# Create your personal dice machine
rng = np.random.default_rng()

# Roll one dice (number between 0 and 1)
print(rng.random())
# Output: 0.7382719...

The Old Way vs The New Way

NumPy has two ways to make random numbers:

Always use the new way!

# NEW WAY - Create your own generator
rng = np.random.default_rng()
number = rng.random()

# OLD WAY - Don't use this anymore
old_number = np.random.rand()

📦 Generating Random Arrays

Making Many Dice at Once

Why roll one dice when you can roll hundreds? NumPy can create entire arrays of random numbers instantly!

rng = np.random.default_rng()

# 5 random numbers between 0 and 1
five_randoms = rng.random(5)
print(five_randoms)
# [0.23, 0.87, 0.12, 0.56, 0.91]

# 3x3 grid of random numbers
grid = rng.random((3, 3))
print(grid)
# [[0.2, 0.5, 0.8],
#  [0.1, 0.9, 0.3],
#  [0.6, 0.4, 0.7]]

Random Integers - Whole Numbers Only

Sometimes you need whole numbers, like dice that show 1, 2, 3, 4, 5, or 6.

rng = np.random.default_rng()

# Roll 10 dice (1 to 6)
dice_rolls = rng.integers(1, 7, size=10)
print(dice_rolls)
# [3, 6, 1, 4, 2, 5, 3, 6, 1, 2]

# Note: 7 is excluded, so we get 1-6

Shape Magic

You can create random arrays in any shape!

rng = np.random.default_rng()

# 1D array: 5 numbers
line = rng.random(5)

# 2D array: 3 rows, 4 columns
table = rng.random((3, 4))

# 3D array: 2 layers, 3 rows, 4 cols
cube = rng.random((2, 3, 4))

🔐 Random Seed Reproducibility

The Time Machine for Random Numbers

Here’s a mind-bending idea: What if you could get the SAME “random” numbers every time you run your code?

That’s what seeds do!

Think of a seed like a secret password. Use the same password, get the same random numbers. Every. Single. Time.

# With seed = 42, you ALWAYS get same result
rng = np.random.default_rng(seed=42)
print(rng.random(3))
# [0.773..., 0.438..., 0.858...]

# Run again with same seed
rng = np.random.default_rng(seed=42)
print(rng.random(3))
# [0.773..., 0.438..., 0.858...]
# SAME NUMBERS!

Why Seeds Matter

graph TD
    A[Same Seed] --> B[Same Random Numbers]
    B --> C[Reproducible Results]
    C --> D[Scientists Can Verify]
    C --> E[Debug Your Code]
    C --> F[Share Experiments]

Real Example:

• Your friend runs your code in Japan
• You run it in Brazil
• Same seed = Same results
• Science can be checked!

📊 Random Sampling Distributions

Not All Randomness is Equal

Imagine throwing darts at a board. Sometimes you aim for the center (normal distribution). Sometimes you throw blindfolded (uniform distribution).

Uniform Distribution

Every number has an equal chance. Like a fair lottery.

rng = np.random.default_rng()

# Numbers between 0 and 1 (uniform)
uniform = rng.uniform(0, 1, size=5)
# [0.23, 0.67, 0.91, 0.12, 0.45]

# Numbers between 10 and 20
scaled = rng.uniform(10, 20, size=5)
# [12.3, 18.7, 11.2, 15.6, 19.1]

Normal Distribution (Bell Curve)

Most values cluster around the middle. Like people’s heights!

rng = np.random.default_rng()

# Average = 170cm, Spread = 10cm
heights = rng.normal(170, 10, size=1000)

# Most people: 160-180cm
# Few people: below 150 or above 190

graph TD
    A[Normal Distribution] --> B[Mean: The Center]
    A --> C[Std Dev: The Spread]
    B --> D[Most values here]
    C --> E[How wide the bell is]

Other Fun Distributions

rng = np.random.default_rng()

# Coin flips: 10 flips, 50% heads
flips = rng.binomial(10, 0.5, size=5)
# [6, 4, 5, 7, 5] heads out of 10

🔀 Random Permutations

Shuffling the Deck

Permutations are about mixing things up. Like shuffling a deck of cards or rearranging a playlist.

Shuffle In Place

Change the original array directly:

rng = np.random.default_rng()

cards = np.array([1, 2, 3, 4, 5])
rng.shuffle(cards)
print(cards)
# [3, 1, 5, 2, 4] - shuffled!

Get a Shuffled Copy

Keep the original, get a new shuffled version:

rng = np.random.default_rng()

original = np.array([1, 2, 3, 4, 5])
shuffled = rng.permutation(original)

print(original)  # [1, 2, 3, 4, 5] - unchanged!
print(shuffled)  # [4, 2, 5, 1, 3] - new order!

Random Sampling (Pick Some Items)

Pick a few items randomly without repetition:

rng = np.random.default_rng()

lottery = np.array([1,2,3,4,5,6,7,8,9,10])

# Pick 3 winners (no repeats)
winners = rng.choice(lottery, size=3, replace=False)
print(winners)
# [7, 2, 9]

With replacement (same item can be picked again):

# Pick 5 with replacement
picks = rng.choice(lottery, size=5, replace=True)
# [3, 7, 3, 1, 9] - 3 appears twice!

🧠 Quick Summary

graph LR
    A[NumPy Random] --> B[Generate Numbers]
    A --> C[Control with Seeds]
    A --> D[Choose Distributions]
    A --> E[Shuffle & Sample]

    B --> B1[random - floats 0-1]
    B --> B2[integers - whole numbers]

    C --> C1[Same seed = Same numbers]

    D --> D1[uniform - equal chance]
    D --> D2[normal - bell curve]

    E --> E1[shuffle - mix in place]
    E --> E2[permutation - get copy]
    E --> E3[choice - pick items]

🚀 Pro Tips

1. Always create your own generator

   rng = np.random.default_rng()
   

2. Use seeds for reproducibility

   rng = np.random.default_rng(seed=42)
   

3. Shape matters! Pass tuples for multi-dimensional arrays

   rng.random((3, 4))  # 3 rows, 4 columns
   

4. Choose the right distribution for realistic data

5. Use replace=False when you need unique selections

You now have the power to generate any random data you need! Go forth and roll those digital dice! 🎲✨