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<h3>Functional relationships for <script type="math/tex">\\\\X \sim Poisson(\lambda),\;\;\lambda \in [0,\infty), x=0,1,...;</script>
</h3>
$$
\\begin{aligned}
p(x|\\lambda)&=\\frac{e^{-\\lambda}\\lambda^{x}}{x!}\\\\\\\\
F(x|\\lambda)&=\\sum_{i=0}^{x}\\left(\\frac{e^{-\\lambda}\\lambda^{i}}{i!}\\right)\\\\\\\\
h(x)&=\\frac{\\lambda{e}^{-\\lambda{t}}}{e^{-\\lambda{t}}}=\\lambda\\\\\\\\\\
E[X]&=\\lambda\\\\\\\\
Var[X]&=\\lambda
\\end{aligned}
$$
