Let $M_X (t)$ be a moment generating function.
These are the things I know:
$Mean=E[X] =M'_X(t)$ at $t=0$ (likewise the second expected value is the second derivative evaluated at $t=0$)
$V[X] = E[X^2] - E[X] $ (where V = Variance)
I have a been given a pdf:
$f_x(x) = x$ if $ 0 \le x \le 1$
$f_x(x) = 2-x$ if $ 1 \le x \le 2$
$f_x(x) = 0$ otherwise
From which I calculated a moment generating function:
$M_x(t) = (\frac {e^t((e^t - 2) + 1)} {t^2})$ so clearly, no matter what derivative I take, if I evaluate this at $t=0$ I get a $0$ in the denominator which is undefined.
The question then asks for the expected value and variance of this distribution. How do I get this?