1. The problem asks: What is a random variable? 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 theory to quantify outcomes and analyze probabilities. 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, with possible values $1, 2, 3, 4, 5, 6$. 6. The random variable helps in calculating probabilities, expected values, variances, and other statistical measures. 7. In summary, a random variable is a numerical representation of outcomes from a random process, essential for probabilistic and statistical analysis.