X follows a discrete uniform distribution over the \(n\) numbers \(\{a, a+1\), \(\ldots, b-1, b\}\) if \(P(X=c)=1 / n\) whenever \(c\) is in the list, and 0 otherwise. Use the rules from chap. 7 to answer the problems below.

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

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

(c) Sketch the probability distribution function (pdf) \(f(x)\), and the cumulative probability distribution function (CDF) \(F(x)\) for the uniform distribution.