Solution
= Solution
Since $2$ lies inside the radius $14/5$ of the <probability generating function>, its nonnegative <series> converges at $2$, and
$$
\boxed{\mathbb E(2^T)=g(2)=\frac23+\frac12=\frac76.}
$$
= Solution
Since $2$ lies inside the radius $14/5$ of the <probability generating function>, its nonnegative <series> converges at $2$, and
$$
\boxed{\mathbb E(2^T)=g(2)=\frac23+\frac12=\frac76.}
$$