How to easily identify different probability distributions? I am studying currently further option mathematics but i cant identify which distribution to utilize in which question? (these are genearlly word questions?)
We are currently studying geometric,poisson, binomial, negative binomial. I was wondering if someone can explain how to identify which problem uses which distribution?
 A: Ask yourself what thing among what things the random variable counts .

A geometric distribution is that of a count of trials until the first success, in a indefinite sequence of independent Bernoulli trials with identical success rate.   This has a support of $\{1,2,\ldots\}$.
$$X\sim \mathcal{Geo}_1(p)\iff \mathsf P(X=k) = (1-p)^{k-1}p\cdot\mathbf 1_{k\in\{1,2,\ldots\}}$$
Sometime a text might define a geometric distribution as that of a count of failures before the first success, in an indefinite sequence of independent Bernoulli trials with identical success rate.   This has a support of $\{0,1,\ldots\}$.
$$X\sim \mathcal{Geo}_0(p)\iff \mathsf P(X=k) = (1-p)^{k}p\cdot\mathbf 1_{k\in\{0,1,\ldots\}}$$
Note: I like to use the subscript to be clear about which geometric distribution I'm taking about.

A binomial distribution is that of the count of successes among a specified number of independent Bernoulli trials with identical success rate. 
$$X\sim\mathcal{Bin}(n,p) \iff \mathsf P(X=k)~=~\binom n k p^k(1-p)^{n-k}\cdot\mathbf 1_{k\in\{0,\ldots, n\}}$$

A negative binomial distribution is that of the count of successes before a specified number of failures, in an indefinite sequence of independent Bernoulli trials with identical success rate.
$$X\sim\mathcal {NegBin}(r,p)\iff \mathsf P(X=k) = \binom{k+r-1}{k}p^k(1-p)^r\cdot\mathbf 1_{k\in\{0,1,\ldots\}}$$
Also, there are relations between Geometric and certain Negative Binomial distributions, $X\sim\mathcal{NegBin}(1,p)\iff X\sim\mathcal{Geo}_0(1-p)$, and so forth.

A Poisson distribution is that of the count of events within an interval that occur at a constant average rate independent of proximity to other events of the process.
$$X\sim\mathcal{Poiss}(\lambda) \iff \mathsf P(X=k) ~=~\dfrac{\lambda ^k ~e ^{-\lambda}}{k!}\cdot\mathbf 1_{k\in\{0,1,\ldots\}}$$
A: Binomial distributions are used for boolean variables, i.e. variables where they can either be true/false, negative binomial is used to model the number of successes(true) before a specified number of failures. Geometric distribution has two different types (https://en.wikipedia.org/wiki/Geometric_distribution). Taking the first definition, its used to describe how many trials you would expect to do before you had your first success. The Poisson distribution is used to describe the number of 'events' you would observe in a given time.
