Random variables are fundamental to understanding probability and statistics. In simple terms, a random variable is a numerical description of the outcome of a random phenomenon. When performing Monte Carlo simulations or any probabilistic experiment, random variables play a central role in modeling various scenarios or events.
To give you a better perspective, random variables can either be discrete or continuous:
- Discrete random variables take on a countable number of values. An example might be the roll of a dice, which can result in one of six possible outcomes.
- Continuous random variables, on the other hand, can take on an infinite number of values within a given range, such as the weight or height of a person.
In our exercise, we focus on continuous random variables, specifically uniform random variables, which are pivotal in random number generation techniques for Monte Carlo simulations.