NumPy: Random Numbers

Last updated: 2026-08-26

1. What You'll Learn

• ❶ The modern default_rng Generator API
• ❷ Common distributions: uniform, normal, integer, choice
• ❸ Seeding for reproducibility
• ❹ Random sampling: with/without replacement
• ❺ Old vs new API

2. Story

Alice runs a Monte Carlo simulation for a financial model. She gets different results every time — impossible to debug. Bob shows her: "Use default_rng(42) — the same seed always produces the same sequence. Debug with seed, deploy without." Alice fixes her seed, finds the bug in 5 minutes.

3. The Modern Generator API

(1) Creating a Generator

import numpy as np

# Modern way (recommended)
rng = np.random.default_rng(42)  # seed = 42 for reproducibility

# Old way (legacy)
np.random.seed(42)

(2) Common Distributions

rng = np.random.default_rng(42)

print(rng.random(3))        # 3 uniform [0, 1)
print(rng.normal(0, 1, 3))  # 3 standard normal
print(rng.integers(0, 10, 5))  # 5 integers [0, 10)
print(rng.uniform(0, 10, 3))   # 3 uniform [0, 10)

> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.

(3) Random Sampling

rng = np.random.default_rng(42)
data = np.arange(10)

# With replacement
sample = rng.choice(data, size=5, replace=True)

# Without replacement
sample2 = rng.choice(data, size=5, replace=False)

# Shuffle
rng.shuffle(data)  # in-place shuffle

> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.

▶ Example: Generating random distributions (Difficulty ⭐)

import numpy as np

rng = np.random.default_rng(42)

uniform = rng.random(5)
normal = rng.normal(0, 1, 5)
integers = rng.integers(1, 100, 5)

print("Uniform [0,1):", uniform)
print("Normal N(0,1):", normal)
print("Integers 1-99:", integers)

Output:

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Uniform [0,1): [0.77395605 0.43887844 0.85859792 0.69736803 0.09417735]
Normal N(0,1): [-0.45938412 -0.19865146  0.1113586  -1.00408446  2.02558468]
Integers 1-99: [79 64 66 81 96]

▶ Example: Random sampling with and without replacement (Difficulty ⭐⭐)

import numpy as np

rng = np.random.default_rng(42)
data = np.arange(20)

# With replacement — same element can appear multiple times
with_repl = rng.choice(data, size=10, replace=True)
print("With replacement:", with_repl)

# Without replacement — all elements are unique
without_repl = rng.choice(data, size=10, replace=False)
print("Without replacement:", without_repl)

# Shuffle in-place
rng.shuffle(data)
print("Shuffled data:", data)

Output:

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With replacement: [ 6 19  9 12  6 15  0  7  3 14]
Without replacement: [13 10  8 11  5  1  9 16 18  4]
Shuffled data: [ 8  7 13 10 18  3 15  5 14 16  0  9  2  1 11 17 12 19  6  4]

▶ Example: Reproducible sequences with seeds (Difficulty ⭐)

import numpy as np

# Same seed = same sequence
rng1 = np.random.default_rng(123)
rng2 = np.random.default_rng(123)

print("rng1:", rng1.random(4))
print("rng2:", rng2.random(4))

# Different seed = different sequence
rng3 = np.random.default_rng(456)
print("rng3:", rng3.random(4))

Output:

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rng1: [0.18701985 0.68208779 0.60135938 0.51034031]
rng2: [0.18701985 0.68208779 0.60135938 0.51034031]
rng3: [0.59831648 0.72572267 0.04819845 0.35980509]

❓ FAQ

📖 Summary

• Use np.random.default_rng(seed) for the modern Generator API
• Common distributions: random, normal, integers, uniform, choice
• Seed your RNG for reproducible results
• shuffle modifies in-place; choice samples with/without replacement
• The old np.random.seed() still works but is legacy — prefer default_rng

📝 Exercises

1. Beginner (Difficulty ⭐): Use default_rng(42) to generate 10 random floats, 10 random integers (0-100), and 10 numbers from a normal distribution. Print them.

2. Intermediate (Difficulty ⭐⭐): Generate 1000 random numbers from a normal distribution. Compute their mean and std. Verify they're approximately 0 and 1.

3. Advanced (Difficulty ⭐⭐⭐): Use rng.choice with and without replacement to sample 10 items from a dataset of 100. Explain the difference and when you'd use each.

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