Solution
= Solution
Differentiate the <probability generating function>:
$$
g'(z)=\frac52(14-5z)^{-3/2},\qquad
g''(z)=\frac{75}4(14-5z)^{-5/2}.
$$
Therefore
$$
\mathbb ET=g'(1)=\frac5{54},\qquad
\mathbb E[T(T-1)]=g''(1)=\frac{25}{324}.
$$
Using the relation between the second factorial moment and <variance>,
$$
\boxed{\operatorname{Var}(T)=g''(1)+g'(1)-g'(1)^2
=\frac{235}{1458}.}
$$