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
When you examine the form of the binomial distribution function:
it is a rather formidable collection of symbols and factorials. These terms arise from an examination of the probability of discrete events. Perhaps the following summary will be helpful:
Index