I am given a PDF
$f_y(y) = 4ye^{-2y}$ for $0<y<\infty$
and have to compute the mgf.
So I did
$M_y(t) = \int_{0}^{\infty}{e^{ty}4ye^{-2y}}$
Which solves to
$M_y(t) = -\frac{4}{{(t-2)}^2}$
Yet according to my book it's
$M_y(t) = \frac{4}{{(t-2)}^2}$
Am I wrong? I redid my calculations a few times.
EDIT: I am an idiot, forgot the $-$ for the lower bound of the integral...
It is solved and can be closed.