Let [f(x)=0.40left(begin{array}{l}4 xend{array} ight) quad text { for } x=0,1,2,3,4] (a) Find the moment generating function. (b) Obtain (E(X)) and (Eleft(X^{2} ight)) by differentiating the

Let

\[f(x)=0.40\left(\begin{array}{l}4 \\x\end{array}\right) \quad \text { for } x=0,1,2,3,4\]

(a) Find the moment generating function.

(b) Obtain \(E(X)\) and \(E\left(X^{2}\right)\) by differentiating the moment generating function.