6. Compute E[X] if X has a density function given by

(a) $$f(x) = \begin{cases}

\frac{1}{4}xe^{-x/2} & x > 0 \\

0 & otherwise

\end{cases}$$

(b) $$f(x) = \begin{cases}

c(1-x^2) & -1 < x < 1 \\

0 & otherwise

\end{cases}$$

(c) $$f(x) = \begin{cases}

\frac{5}{2} & x > 5 \\

0 & x \le 5

\end{cases}$$