Consider three independent uniformly distributed (taking values between $0$ and $1$) random variables. What is the probability that the middle of the three values (between the lowest and the highest value) lies between $a$ and $b$ where $0 ≤ a < b ≤ 1$.
- $3 (1 - b) a (b - a)$
- $3 (b - a) - (b^{2}- a^{2})/2)$
- $6 (1 - b) a (b - a)$
- $(1 - b) a (b - a)$
- $6 ((b^{2}- a^{2})/ 2 - (b^{3} - a^{3})/3)$.