Which of the following correctly states the two defining properties of a probability density function (PDF) f(x) for a continuous random variable X?

f(x) can be negative if it integrates to 1 over its support, provided the negative regions are offset by larger positive regions so the net integral is 1

f(x) ≥ 0 for all x, and ∫_{-∞}^{∞} f(x) dx = 100 percent when probabilities are expressed as percentages (i.e., 100%), so the integral equals 100 rather than 1 if using percentage units

f(x) ≥ 0 for all x, and ∫_{-∞}^{∞} f(x) dx = 1

f(x) ≥ 0 for all x and F(x) = ∫_{-∞}^{x} f(t) dt must equal zero for x less than all possible outcomes