X follows a continuous uniform probability distribution over the interval \(I=(a, b)\) if \(P(X=x)=1 /(b-a)\) whenever \(x \in I\), and 0 otherwise. Use the rules from sections 7.3, 7.5 and 7.6 to solve the problems below:

(a) Find \(\mu_{X}\).

(b) Find \(\sigma_{X}^{2}\).

(c) Graph the probability distribution \(f(x)\) and the cumulative probability distribution \(F(x)\) of the continuous uniform probability distribution.