\item \subquestionpoints{5} Consider the Poisson distribution parameterized by
$\lambda$:
%
\begin{equation*}
  p(y; \lambda) = \frac{e^{-\lambda}\lambda^y}{y!}.
\end{equation*}
%
(Here $y$ has positive integer values and $y!$ is the factorial of $y$. ) 
Show that the Poisson distribution is in the exponential family, and
clearly state the values for $b(y)$, $\eta$, $T(y)$, and $a(\eta)$.