Random Number Generator

Created:December 22, 2024

Last Updated:December 22, 2024

Generate random numbers from probability distributions (uniform, normal, binomial) or sample from custom lists. Ideal for simulations, Monte Carlo methods, statistical analysis, and randomization tasks. Set seeds for reproducibility, visualize distributions with histograms, and export data for use in spreadsheets or statistical software.

Calculator

Parameters

Random Seed (optional, for reproducibility)

Leave empty for truly random results

Population (comma-separated)

Sample Size

Max: 10,000 samples

Sample with replacement

Sample Results

Click Generate to see your random sample

Related Calculators

Binomial Distribution Calculator

Normal Distribution Calculator

Uniform Distribution Calculator

Sample Size Calculator

Learn More

Random Sampling Methods

Random sampling is a technique where each member of a population has an equal chance of being selected. This ensures unbiased samples and enables valid statistical inference in research, surveys, and experiments.

Two Sampling Methods:

With Replacement: After selecting an item, it's returned to the population and can be selected again. Useful for bootstrap methods and theoretical sampling distributions.
Without Replacement: Once an item is selected, it cannot be selected again in the same sample. Common in surveys and experimental random assignment.

Available Probability Distributions

Currently supports three fundamental distributions, with more distributions (exponential, Poisson, chi-square, t-distribution, etc.) coming soon.

Uniform Distribution:

All values in a range are equally likely. Useful for generating random numbers between two bounds or simulating equally probable outcomes.

f(x) = \begin{cases} \frac{1}{b-a} & a \leq x \leq b \\ 0 & \text{otherwise} \end{cases}

Normal Distribution:

The bell curve distribution. Most values cluster around the mean, with fewer values farther away. Fundamental to the Central Limit Theorem and most statistical inference.

f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}

Binomial Distribution:

Models the number of successes in n independent trials, each with probability p. Common in quality control, genetics, and success/failure experiments.

P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}

Why Use a Seed?

A random seed initializes the random number generator to produce a specific sequence of "random" numbers. Using the same seed will always produce the same sequence, which is essential for:

Reproducible research and experiments
Debugging simulations and code
Sharing results that others can verify
Testing and validation of statistical methods
Educational demonstrations and tutorials

Common Use Cases

This random number generator is useful for:

Monte Carlo Simulations: Estimate probabilities and model complex systems through random sampling
Statistical Sampling: Practice sampling techniques and study sampling distributions
Hypothesis Testing: Generate null distributions for permutation and bootstrap tests
Data Science: Create synthetic datasets for testing algorithms and models
Education: Teach probability concepts and statistical distributions (AP Statistics, university courses)
Random Assignment: Assign subjects to treatment groups in experimental design

Random Sampling in R

library(tidyverse)

# Parameters
population <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
sample_size <- 5
with_replacement <- FALSE

# Set seed for reproducibility
set.seed(42)

# Sample from population
sample_data <- sample(population, size = sample_size, replace = with_replacement)
print(sample_data)

Random Sampling in Python

Python

import numpy as np

# Parameters
population = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
sample_size = 5
with_replacement = False

# Set seed for reproducibility
np.random.seed(42)

# Sample from population
sample_data = np.random.choice(population, size=sample_size, replace=with_replacement)
print(sample_data)

Distribution Generation in R

library(tidyverse)

# Set seed for reproducibility
set.seed(42)

# Normal distribution
normal_sample <- rnorm(n = 100, mean = 50, sd = 10)
print(head(normal_sample))
print(paste("Mean:", round(mean(normal_sample), 2)))
print(paste("SD:", round(sd(normal_sample), 2)))

# Uniform distribution
uniform_sample <- runif(n = 100, min = 0, max = 100)

# Binomial distribution
binomial_sample <- rbinom(n = 100, size = 10, prob = 0.5)

# Histogram
hist(normal_sample, main = "Normal Distribution Sample",
     xlab = "Value", col = "lightblue", breaks = 20)

Distribution Generation in Python

Python

import numpy as np
import matplotlib.pyplot as plt

# Set seed for reproducibility
np.random.seed(42)

# Normal distribution
normal_sample = np.random.normal(loc=50, scale=10, size=100)
print(f"Mean: {np.mean(normal_sample):.2f}")
print(f"SD: {np.std(normal_sample, ddof=1):.2f}")

# Uniform distribution
uniform_sample = np.random.uniform(low=0, high=100, size=100)

# Binomial distribution
binomial_sample = np.random.binomial(n=10, p=0.5, size=100)

# Histogram
plt.hist(normal_sample, bins=20, color='lightblue', edgecolor='black')
plt.title('Normal Distribution Sample')
plt.xlabel('Value')
plt.ylabel('Frequency')
plt.show()

Random Number Generator

Created:December 22, 2024

Last Updated:December 22, 2024

Calculator

Parameters

Random Seed (optional, for reproducibility)

Leave empty for truly random results

Population (comma-separated)

Sample Size

Max: 10,000 samples

Sample with replacement

Sample Results

Click Generate to see your random sample

Related Calculators

Binomial Distribution Calculator

Normal Distribution Calculator

Uniform Distribution Calculator

Sample Size Calculator

Learn More

Random Sampling Methods

Two Sampling Methods:

With Replacement: After selecting an item, it's returned to the population and can be selected again. Useful for bootstrap methods and theoretical sampling distributions.
Without Replacement: Once an item is selected, it cannot be selected again in the same sample. Common in surveys and experimental random assignment.

Available Probability Distributions

Currently supports three fundamental distributions, with more distributions (exponential, Poisson, chi-square, t-distribution, etc.) coming soon.

Uniform Distribution:

All values in a range are equally likely. Useful for generating random numbers between two bounds or simulating equally probable outcomes.

f(x) = \begin{cases} \frac{1}{b-a} & a \leq x \leq b \\ 0 & \text{otherwise} \end{cases}

Normal Distribution:

The bell curve distribution. Most values cluster around the mean, with fewer values farther away. Fundamental to the Central Limit Theorem and most statistical inference.

f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}

Binomial Distribution:

Models the number of successes in n independent trials, each with probability p. Common in quality control, genetics, and success/failure experiments.

P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}

Why Use a Seed?

A random seed initializes the random number generator to produce a specific sequence of "random" numbers. Using the same seed will always produce the same sequence, which is essential for:

Reproducible research and experiments
Debugging simulations and code
Sharing results that others can verify
Testing and validation of statistical methods
Educational demonstrations and tutorials

Common Use Cases

This random number generator is useful for:

Monte Carlo Simulations: Estimate probabilities and model complex systems through random sampling
Statistical Sampling: Practice sampling techniques and study sampling distributions
Hypothesis Testing: Generate null distributions for permutation and bootstrap tests
Data Science: Create synthetic datasets for testing algorithms and models
Education: Teach probability concepts and statistical distributions (AP Statistics, university courses)
Random Assignment: Assign subjects to treatment groups in experimental design

Random Sampling in R

library(tidyverse)

# Parameters
population <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
sample_size <- 5
with_replacement <- FALSE

# Set seed for reproducibility
set.seed(42)

# Sample from population
sample_data <- sample(population, size = sample_size, replace = with_replacement)
print(sample_data)

Random Sampling in Python

Python

import numpy as np

# Parameters
population = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
sample_size = 5
with_replacement = False

# Set seed for reproducibility
np.random.seed(42)

# Sample from population
sample_data = np.random.choice(population, size=sample_size, replace=with_replacement)
print(sample_data)

Distribution Generation in R

library(tidyverse)

# Set seed for reproducibility
set.seed(42)

# Normal distribution
normal_sample <- rnorm(n = 100, mean = 50, sd = 10)
print(head(normal_sample))
print(paste("Mean:", round(mean(normal_sample), 2)))
print(paste("SD:", round(sd(normal_sample), 2)))

# Uniform distribution
uniform_sample <- runif(n = 100, min = 0, max = 100)

# Binomial distribution
binomial_sample <- rbinom(n = 100, size = 10, prob = 0.5)

# Histogram
hist(normal_sample, main = "Normal Distribution Sample",
     xlab = "Value", col = "lightblue", breaks = 20)

Distribution Generation in Python

Python

import numpy as np
import matplotlib.pyplot as plt

# Set seed for reproducibility
np.random.seed(42)

# Normal distribution
normal_sample = np.random.normal(loc=50, scale=10, size=100)
print(f"Mean: {np.mean(normal_sample):.2f}")
print(f"SD: {np.std(normal_sample, ddof=1):.2f}")

# Uniform distribution
uniform_sample = np.random.uniform(low=0, high=100, size=100)

# Binomial distribution
binomial_sample = np.random.binomial(n=10, p=0.5, size=100)

# Histogram
plt.hist(normal_sample, bins=20, color='lightblue', edgecolor='black')
plt.title('Normal Distribution Sample')
plt.xlabel('Value')
plt.ylabel('Frequency')
plt.show()

library(tidyverse) # Parameters population <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10) sample_size <- 5 with_replacement <- FALSE # Set seed for reproducibility set.seed(42) # Sample from population sample_data <- sample(population, size = sample_size, replace = with_replacement) print(sample_data)

import numpy as np # Parameters population = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] sample_size = 5 with_replacement = False # Set seed for reproducibility np.random.seed(42) # Sample from population sample_data = np.random.choice(population, size=sample_size, replace=with_replacement) print(sample_data)

library(tidyverse) # Set seed for reproducibility set.seed(42) # Normal distribution normal_sample <- rnorm(n = 100, mean = 50, sd = 10) print(head(normal_sample)) print(paste("Mean:", round(mean(normal_sample), 2))) print(paste("SD:", round(sd(normal_sample), 2))) # Uniform distribution uniform_sample <- runif(n = 100, min = 0, max = 100) # Binomial distribution binomial_sample <- rbinom(n = 100, size = 10, prob = 0.5) # Histogram hist(normal_sample, main = "Normal Distribution Sample", xlab = "Value", col = "lightblue", breaks = 20)

import numpy as np import matplotlib.pyplot as plt # Set seed for reproducibility np.random.seed(42) # Normal distribution normal_sample = np.random.normal(loc=50, scale=10, size=100) print(f"Mean: {np.mean(normal_sample):.2f}") print(f"SD: {np.std(normal_sample, ddof=1):.2f}") # Uniform distribution uniform_sample = np.random.uniform(low=0, high=100, size=100) # Binomial distribution binomial_sample = np.random.binomial(n=10, p=0.5, size=100) # Histogram plt.hist(normal_sample, bins=20, color='lightblue', edgecolor='black') plt.title('Normal Distribution Sample') plt.xlabel('Value') plt.ylabel('Frequency') plt.show()