Currently I'm trying to approach a question whereby I am trying to obtain the Probability Density Function from the Moment Generating Function as follow: $$M_Y(t)=\left(\frac{e^t-1}{t} \right)^2$$
It looks like a uniform distribution with b=1 and a=0 but with the square being there, I am unable to proceed from here. $$M(t)=\frac{e^{tb}-e^{ta}}{t(b-a)} $$
Any help or advice would be appreciated.
-Kevin-
Hint: Given independent random variables $X$ and $Y$, the moment generating function of $Z=X+Y$ is $$M_Z(t)=M_X(t)M_Y(t)$$ where $M_X(t)$ and $M_Y(t)$ are the moment generating function of $X$ and $Y$.
What should we do with the pdf of two independent random variables to get the pdf of their sum?