How would I go about finding the probability of a random variable based on its piece-wise CDF?
For example, I'm trying to find $P(X > 0.5)$ and $P(0.2 < X < 0.8)$ of
$$F_X(x) = \begin{cases} 0 & x \leq 0 \\ x^3 & 0 \leq x \leq 1 \\ 1 & x \geq 1 \end{cases}$$