Recall that a random variable $X$, taking values in $\mathbb{N}$, follows the Poisson distribution $\mathcal{P}(\lambda)$ with parameter $\lambda$ if, for all $n \in \mathbb{N}$:
$$\mathrm{P}(X = n) = \frac{\lambda^{n}}{n!} \mathrm{e}^{-\lambda}$$
Let $X$ be a random variable that follows the Poisson distribution $\mathcal{P}(\lambda)$. Calculate the expectation $\mathrm{E}(X)$, the variance $V(X)$ and the standard deviation of $X$.