For a continuous random variable X with PDF f(x), which of the following statements is true regarding the probability that X equals an exact number a (i.e., P(X = a))?

Let f(x) = a x^2 for 0 ≤ x ≤ 2 and f(x)=0 otherwise. Find the value of a that makes f a valid PDF.

Using the CDF F(x)=1 - e^{-x^3} for x ≥ 0 derived from f(x)=3x^2 e^{-x^3}, compute P(1 ≤ X ≤ 3).