# Binomial Distribution Function Distribution | Functional Form | Mean | Standard Deviation | Binomial | | | |
The binomial distribution function specifies the number of times (x) that an event occurs in n independent trials where p is the probability of the event occurring in a single trial. It is an exact probability distribution for any number of discrete trials. If n is very large, it may be treated as a continuous function. This yields the Gaussian distribution. If the probability p is so small that the function has significant value only for very small x, then the function can be approximated by the Poisson distribution. With the parameters as defined above, the conditions for validity of the binomial distribution are - each trial can result in one of two possible outcomes, which could be characterized as "success" or "failure".
- the probability of "success", p, is constant from trial to trial.
- the trials are independent.
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