If \( X \) is a random variable with the probability mass function (p.m.f.) as follows:
\[
P(X = x) = \begin{cases}
\frac{5}{16}, & x = 0, \\
\frac{kx}{48}, & x = 1, \\
\frac{1}{4}, & x = 2, \\
\frac{1}{4}, & x = 3,
\end{cases}
\]
then find \( E(X) \):