If $(x_1,\cdots, x_n)$ is a sample from a Poisson(θ) distribution, where $θ ∈ (0,∞)$ is unknown, then determine the $MLE$ of $θ$.
my attempt:
so the probability density of poisson is
$$p_{\theta}(x) = \frac{\theta^x e^{-\theta}}{x!}$$
the likelihood is given by
$L(\theta | \bar{x}) = \prod_{i=1}^{n} \frac{\theta^{x_i}e^{-\theta}}{x_i!} = e^{-n\theta} \left(\prod_{i=1}^{n} \frac{1}{x_i!} \right) \theta^{\sum_{i=1}^{n}x_i}$
How do I do the factorial ?
For some reason in the solution their answer is just $e^{-n\theta} \theta^{\sum_{i=1}^{n}x_i}$ ?