NumPy Random Module

import numpy as np

# Seed for reproducibility (same seed → same random numbers)
rng = np.random.default_rng(seed=42)  # Modern API (recommended)

# Or legacy API:
np.random.seed(42)

# Uniform random floats [0.0, 1.0)
print(rng.random(5))           # 5 random floats

# Random integers
print(rng.integers(1, 100, 5)) # 5 integers between 1-99
print(rng.integers(1, 7, (3, 4)))  # 3x4 matrix, dice values 1-6

# Standard normal distribution (mean=0, std=1)
print(rng.standard_normal(5))  # 5 normally distributed values

# Normal with custom mean and std
print(rng.normal(loc=170, scale=10, size=5))  # Heights: mean 170cm, std 10

rng = np.random.default_rng(42)

# Uniform distribution
uniform = rng.uniform(low=0, high=100, size=1000)

# Normal (Gaussian) distribution — bell curve
normal = rng.normal(loc=0, scale=1, size=1000)

# Binomial (n trials, probability p)
binomial = rng.binomial(n=10, p=0.5, size=1000)  # Coin flips

# Poisson (events per interval)
poisson = rng.poisson(lam=5, size=1000)  # 5 events per hour average

# Exponential (time between events)
exponential = rng.exponential(scale=2.0, size=1000)

# Beta (0-1, useful for probabilities)
beta = rng.beta(a=2, b=5, size=1000)

# Print distribution stats
for name, dist in [('Normal', normal), ('Binomial', binomial), ('Poisson', poisson)]:
    print(f"{name}: mean={np.mean(dist):.2f}, std={np.std(dist):.2f}")

rng = np.random.default_rng(42)
data = np.arange(1, 21)   # [1, 2, ..., 20]

# Random choice (with replacement)
sample_with = rng.choice(data, size=5, replace=True)
print("With replacement:", sample_with)

# Random choice (without replacement)
sample_without = rng.choice(data, size=5, replace=False)
print("Without replacement:", sample_without)

# Shuffle in-place
arr = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
rng.shuffle(arr)
print("Shuffled:", arr)

# Permutation (returns new shuffled array)
original = np.arange(10)
shuffled = rng.permutation(original)
print("Permuted:", shuffled)

# Weighted random choice
items = np.array(['apple', 'banana', 'cherry'])
weights = np.array([0.5, 0.3, 0.2])  # Probabilities (must sum to 1)
sample = rng.choice(items, size=10, p=weights)
print("Weighted:", np.unique(sample, return_counts=True))

import numpy as np

rng = np.random.default_rng(42)

# Simulation 1: Monte Carlo estimate of π
n_points = 1_000_000
x = rng.uniform(-1, 1, n_points)
y = rng.uniform(-1, 1, n_points)
inside_circle = (x**2 + y**2) <= 1
pi_estimate = 4 * np.sum(inside_circle) / n_points
print(f"π estimate: {pi_estimate:.4f}")  # ~3.1416

# Simulation 2: Stock price simulation (random walk)
n_days = 252  # Trading days in a year
daily_returns = rng.normal(loc=0.0005, scale=0.02, size=n_days)
price = 100 * np.cumprod(1 + daily_returns)
print(f"Final stock price: ${price[-1]:.2f}")
print(f"Return: {(price[-1]/100 - 1)*100:.1f}%")

# Simulation 3: Bootstrap confidence interval
data = np.array([34, 45, 67, 23, 78, 56, 89, 45, 34, 67])
n_bootstrap = 10000
bootstrap_means = [rng.choice(data, len(data), replace=True).mean()
                   for _ in range(n_bootstrap)]
bootstrap_means = np.array(bootstrap_means)
ci_lower = np.percentile(bootstrap_means, 2.5)
ci_upper = np.percentile(bootstrap_means, 97.5)
print(f"95% CI for mean: [{ci_lower:.1f}, {ci_upper:.1f}]")