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We call a distribution a binomial distribution if all of the following are true

1. There are a fixed number of trials, n, which are all independent.

2. There must be exactly two mutually exclusive outcomes in a trial, such as True of False, yes or no, success or failure.

3. The probability of success is the same for each trial.

There are various applications for binomial distributions. Binomial distributions describe the possible number of times that a particular event will occur in a sequence of observations. They are used when we want to know about the occurrence of an event, not its magnitude. Binomial distributions are used in various number of places. In a clinical trial, a patient’s condition may improve or not. We study the number of patients who improved, not how much better they feel. In checking if a person is ambitious or not, the binomial distribution describes the number of ambitious persons, not how ambitious they are. In quality control we assess the number of defective items in a lot of goods, irrespective of the type of defect.

The notation of Binomial distribution is X ~B(n,p).

Where n is a fixed number of trials, the outcome of a given trial is either a success or failure and probability of success (p) remains constant from trial to trial.

The major courses included in Binomial Distribution are sum of binomials, conditional binomials, Bernoulli distribution, Poisson binomial distribution, Normal approximation, Poisson approximation, Limiting distributions, Beta distribution etc.