Given a discrete random variable X with f(x) as follows: \\[0.5em] \begin{array}{c|ccccc} x & 0 & 1 & 2 & 3 & 4 \\ \hline f(x) & 0.1 & 0.2 & 0.4 & 0.2 & 0.1 \end{array} \\[0.5em] (a) Find the moment generating function of X, M_X(t). \\[0.5em] (b) Use the M_X(t) obtained in (a) to calculate: (i) E(X), (ii) V(X).