Understanding Random Variables

Random numbers are fundamental in modeling noise and uncertainty in real-world processes. The nature of randomness varies according to the underlying phenomena. This experiment aims to help you understand:

1. Different types of probability distributions
2. How to generate random numbers with specific distributions
3. The relationship between probability distributions and real-world phenomena

Example: Rolling Dice

Consider the following examples:

• Rolling a single die: Results vary between 1 to 6, with equal probability
• Rolling two dice: The sum varies between 2 to 12, with different probabilities
  • Getting a 7 is more likely than getting a 2 or 12
  • This is due to the combination of possible outcomes

Computer-Generated Randomness

While nature generates randomness naturally, computers are deterministic machines. This experiment will help you understand:

1. How to generate random numbers on a computer
2. Different methods of random number generation
3. How to transform random numbers to follow specific distributions

Note: Please carefully review the introduction to random numbers and probability densities before starting the experiment.