Methods of Generating Random Numbers

Since computers are deterministic machines, they cannot generate true randomness. There are two main approaches to generate random numbers:

1. Physical Random Number Generation

• Uses physical devices (sensors) to capture natural phenomena
• Converts the readings to digital form
• Provides high-quality randomness
• More expensive and complex to implement
• Used in applications requiring high security or scientific accuracy

2. Pseudorandom Number Generation

• Uses special algorithms called Pseudorandom Number Generators
• Generates sequences that appear random
• More efficient and cost-effective
• Most commonly used method
• Quality depends on the algorithm used

3. Hybrid Approach

• Combines both methods
• Uses operating system parameters as seed for randomness
• Balances between quality and efficiency
• Useful for applications requiring moderate randomness quality

Distribution Transformation

The random numbers generated by any of these methods will follow a specific distribution. To obtain numbers following a desired distribution, we need to:

1. Generate random numbers using one of the above methods
2. Transform these numbers to follow the target distribution
3. Verify the transformed numbers match the desired distribution

Additional Resources

For a detailed understanding of random variables and their properties, please refer to the comprehensive writeup provided here.

Key Concepts to Understand

• Probability distribution functions
• Probability density functions
• Transformation methods
• Quality metrics for random number generation
• Applications of different random number generation methods