One increasing function, F(x) = P(X ≤ x), pins down the whole law of a random variable. The probability P(a < X ≤ b) is the rise of F between a and b, an atom is a jump, and a gap in the values is a flat stretch. Build a distribution here from atoms and a continuous part, then read probabilities straight off the curve. Reading F backwards turns a uniform draw into a draw of X, which is how simulations sample from a law. An insurance claim that is exactly 0 with probability 0.7 and otherwise a continuous amount is neither discrete nor continuous, yet F describes it without fuss.