A random variable \(U\) is uniformly distributed on the interval \((-A, A)\) and its probability density function is zero otherwise.

(a) Find an expression for \(A\) in terms of the variance \(\sigma_{U}^{2}\) of \(U\).

(b) Find an expression for the characteristic function of \(U\) as a function of the variance \(\sigma_{U}^{2}\).