Binomial,Geometric,Hypergeometric,Poisson,NegB Distributions

Cited from the Youtube video  Overview of Some Discrete Probability Distributions (Binomial,Geometric,Hypergeometric,Poisson,NegB) 

Binomial, negative binomial and geometric distributions depends on the assumption of independent Bernoulli trials. 

Binomial distribution:
The number of trials is fixed, and the number of successes is the random variable.

Bernoulli distribution:
A special case of binomial distribution, the number of trail is fixed as 1, and the number of successes is the random variable.

Negative binomial distribution:
The number of successes is fixed, and the number of trial is the random variable.

Geometric distribution:
A special case of negative binomial distribution, the number of successes is fixed as 1, and the number of trials is the random variable.

Hypergeometric distribution depends on the assumption of non-independent trials. The drawing is without replacement from a source that contains a certain a certain number of successes and a certain number of failures.

Hypergeometric distribution:
Similar to binomial distributions, the number of trials is fixed, and the number of successes is the random variable.

If objects were sampled from a large population without replacement, the inter-dependence has a small effect. Then the binomial distribution closely approximates the hypergeometric distribution.

Poisson districtuion :
The Poisson distribution models the number of events (the random variable) in a given time, length, area or volume, etc, if these events occur randomly and independently.

The Poisson distribution approximates the Binomial distribution, when the number of trials (n) is large, and p the probability of successes is very small.