Solution
= Solution
The rate-one <exponential distribution> has density $e^{-t}$ for $t\geq0$. <Integration by parts> gives $\mathbb ET=1$ and $\mathbb E[T^2]=2$, so
$$
\boxed{\mathbb ET=1,\qquad\operatorname{Var}(T)=2-1^2=1.}
$$
= Solution
The rate-one <exponential distribution> has density $e^{-t}$ for $t\geq0$. <Integration by parts> gives $\mathbb ET=1$ and $\mathbb E[T^2]=2$, so
$$
\boxed{\mathbb ET=1,\qquad\operatorname{Var}(T)=2-1^2=1.}
$$