Solution
= Solution
Direct integration of the gamma density gives, for $t<1$,
$$
\boxed{M_S(t)=\frac1{(n-1)!}\int_0^\infty s^{n-1}e^{-(1-t)s}\,ds=(1-t)^{-n}.}
$$
= Solution
Direct integration of the gamma density gives, for $t<1$,
$$
\boxed{M_S(t)=\frac1{(n-1)!}\int_0^\infty s^{n-1}e^{-(1-t)s}\,ds=(1-t)^{-n}.}
$$