1. The problem is to understand what random variables are. 2. A random variable is a function that assigns a numerical value to each outcome in a sample space of a random experiment. 3. It is used in probability and statistics to quantify outcomes of random processes. 4. There are two main types: discrete random variables (which take countable values) and continuous random variables (which take values in a continuum). 5. For example, if you roll a fair six-sided die, the random variable $X$ could represent the number shown on the die, taking values $1, 2, 3, 4, 5,$ or $6$. 6. The key formula related to random variables is the expected value (mean), given by $$E(X) = \sum x_i P(X = x_i)$$ for discrete variables, where $x_i$ are possible values and $P(X = x_i)$ their probabilities. 7. Random variables help us model uncertainty and make predictions based on probability distributions.