The binomial distribution, also known as Bernoulli distribution, describes the random sampling processes that all outcomes are either yes or no (success/failure) without ambiguity. In addition, the probability will not change from one trial to another (independent). In this case, the number of total available samples remains the same throughout the sampling process. In other words, the total number of available samples is either infinity or the chosen sample are always placed back to the sampling pool before the next trial (Sampling with replacement).
Suppose that the probability of success in a single trial is in a random sampling process and the failure rate is , where . The binomial distribution with exactly successes in trials, where , has the following important properties. See plots of binomial distributions.
Binomial Distribution 
Density Function  
Distribution Function  
Mean  
Variance  
Standard Deviation  
