I am currently taking a probability and statistics course. We recently started studying discrete random variables, specifically discrete distributions lately. I want to ensure I understand what each of these distributions enables one to compute. Are the following descriptions accurate?
$X\sim\textit{Bernoulli}\left(p\right)$, where $p$ is the probability of a success. The distribution solves the probability of a success in one trial.
$X\sim\textit{Geometric}\left(p\right)$, where $p$ is the probability of a success. The distribution solves the number of trials until a success.
$X\sim\textit{Binomial}\left(n,p\right)$, where $n$ is the number of trials and $p$ is the probability of a success. The distribution solves the number of successes in $n$ trials.
$X\sim\textit{Pascal}\left(m,p\right)$, where $m$ is the number of successes and $p$ is the probability of a success. The distribution solves the number of trials until $m$ successes.
$X\sim\textit{Poisson}\left(\lambda\right)$. I am having some trouble with this one. Could someone please explain?
Thank you!