A random variable has a pdf given by $$ f(x) = \left\{ \begin{array}{ll} x & \quad 0 \leq x<1 \\ 2-x & \quad 1 \leq x < 2 \end{array} \right. $$
I am then told to find the MGF, M(t), which I got $$M(t) = \frac{e^{2t}-2e^t+1}{t^2}$$ and I'm almost certain that this is correct. Then I'm asked to find the value of $M(0)$. I was expecting this to be $1$ given that X is a PDF. But as you can see, $M(0)$ would be undefined. Why doesn't $M(0) = 1$? Also, to answer the question "Find the value of $M(0)$", should I just say that $M(0)$ is undefined?