# Binomial Distribution

## Definition of Binomial Distribution

A binomial distribution is a statistical distribution that gives the probability of a certain number of successes in a series of n independent Bernoulli trials.

## What is Binomial Distribution used for?

Binomial Distribution is a probability distribution that provides the likelihood of observing k successes in n trials, provided the probability of success in a single trial is known. This type of distribution is used to predict the probability of observing a certain number of successes or failures based on a fixed number of trials. It is commonly used in statistical analysis and machine learning applications as it can determine outcomes with binary values, such as yes/no, true/false, or heads/tails.

The Binomial Distribution formula consists of two parameters – the probability of success in each trial (p) and the number of trials (n). The distribution varies from 0 to 1 and is symmetrical around p. It also has two special cases: when p=0 all values will be 0; when p=1 all values will be 1.

In terms of its applications, the Binomial Distribution can be used for predictive analytics by evaluating the likelihood that an event will occur given that it has some probability of happening in each trial. In addition, it’s widely used for risk assessment by providing information about whether an experiment has been successful or not, so that informed decisions can be made accordingly. It’s also useful for hypothesis testing and calculating confidence intervals.