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

Let f(x) = 3x^2 for 0 ≤ x ≤ 1 and 0 otherwise. Compute P(0.2 ≤ X ≤ 0.5).

Given the PDF f(x) = 3x^2 e^{-x^3} for x ≥ 0 and f(x) = 0 for x < 0, compute the cumulative distribution function F(x) for x ≥ 0.

Let f(x) = k(x^2 + x) for 0 ≤ x ≤ 2 and 0 otherwise. (a) Find k. (b) Compute P(0.5 ≤ X ≤ 1.5).

Which statement about the cumulative distribution function (CDF) F(x) of a continuous random variable is always true?