What term describes the long-term average outcome of a random variable?

The term that accurately describes the long-term average outcome of a random variable is the expected value. In probability theory and statistics, the expected value represents the probability-weighted average of all possible values that a random variable can take. It essentially gives us an indication of what we can expect as an average if we were to repeat an experiment or process many times.

For example, if you were to roll a fair six-sided die, the expected value can be calculated by taking the average of all possible outcomes, weighted by their probabilities. In this case, each side has an equal chance of occurring, and the expected value helps to summarize the long-term behavior of rolling the die repeatedly.

In contrast, while the mean is often used interchangeably with expected value in many contexts, expected value is a broader term that applies specifically to random variables. The median is the middle value in a sorted list of numbers, while the mode refers to the most frequently occurring value in a dataset. Hence, neither median nor mode would represent the average outcome of a random variable in the way that expected value does.