| Version 4 |
Version 3 |
| \PMlinkescapeword{events} |
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| \PMlinkescapeword{fields} |
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| \PMlinkescapeword{syntax} |
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| $X$ is a \textbf{Poisson random variable} with parameter \textbf{$\lambda$} if\\ |
$X$ is a \textbf{Poisson random variable} with parameter \textbf{$\lambda$} if\\ |
| \par |
\par |
| $f_X(x) = \frac{e^{-\lambda} \lambda^x}{x!}$, $x=\{0,1,2,...\}$ \\ |
$f_X(x) = \frac{e^{-\lambda} \lambda^x}{x!}$, $x=\{0,1,2,...\}$ \\ |
| \par |
\par |
| Parameters:\\ |
Parameters:\\ |
| \par |
\par |
| \begin{list}{$\star$ }{} |
\begin{list}{$\star$ }{} |
| \item $\lambda > 0$ |
\item $\lambda > 0$ |
| \end{list} |
\end{list} |
| \par |
\par |
| Syntax:\\ |
Syntax:\\ |
| \par |
\par |
| $X\sim Poisson(\lambda)$\\ |
$X\sim Poisson(\lambda)$\\ |
| \par |
\par |
| Notes:\\ |
Notes:\\ |
| \par |
\par |
| \begin{enumerate} |
\begin{enumerate} |
| \item $X$ is often used to describe the ocurrence of rare events. It's a very commonly used distribution in all fields of statistics. |
\item $X$ is often used to describe the ocurrence of rare events. It's a very commonly used distribution in all fields of statistics. |
| \item $E[X] = \lambda$ |
\item $E[X] = \lambda$ |
| \item $Var[X] = \lambda$ |
\item $Var[X] = \lambda$ |
| \item $M_X(t) = e^{\lambda (e^t - 1)}$ |
\item $M_X(t) = e^{\lambda (e^t - 1)}$ |
| \end{enumerate} |
\end{enumerate} |
