random variable

A _quantity whose value is uncertain until it is drawn_ — but whose possible values have a distribution. A coin flip is the random variable `X ∈ {heads, tails}` with `P(X = heads) = 0.5`. A daily stock return is a real-valued random variable with some continuous distribution over `(−∞, ∞)`. Random variables are how probability talks about _quantities_: they have means (the expected value), spread (variance), and they combine into other random variables (sums, products, ratios). The variable is not the distribution — the variable _has_ a distribution. Confusing the two leads to bad math.