Let $x$ be a random variable whose pdf is given by

$f_x(x)=\{\begin{array}{cc}{e}^{-2x}+\frac{1}{2}{e}^{-x},& x>0\\ 0,& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}$

a$.$ Is $f_x(x)$ a pdf $?$

b$.$ Write down the moment generating function for $x$

c$.$ Use this moment generating function to compute the first and

second moment of $x$