# What is the Bernoulli Distribution?

The Bernoulli distribution is a discrete distribution that describes an event with a binary outcome. This outcome can be defined as 0 (usually indicating failure) or 1 (generally meaning success).

Mathematically, the distribution can be defined by a single parameter p that gives the probability that the result is 1 as:

P(x=1) = p

P(x=0) = 1 – p

An example is the toss of a coin, where 1 can represent “heads” and 0 “tails” (or vice versa) and p( probability of landing on heads or tails) = 0.50.

The Bernoulli distribution is the simplest of all discrete distributions, and it is similar to the binomial distribution, but only considering a single yes/no test, known as “Bernoulli trials.” It is also a particular case of the two-point distribution.

Some essential characteristics of the Bernoulli distribution are:

- p must remain constant throughout all trials
- Trials must be independent of each other
- For 0 ≤ p ≤ 1, they form an exponential family
- Probability Mass Function, where k is the number of outcomes.
- Mean: E(X) = p
- Var(X) = p*q = p* (1-p)

It was named after Swiss mathematician Jacob Bernoulli, who developed the Binomial distribution in a posthumous paper in 1973.

### Why is the Bernoulli Distribution Important?

Analytics deals with many problems where data is discrete, such as words and DNA sequences. As such, many problems that have only two possible outcomes can be simulated with the Bernoulli distribution.

Besides, we can think of the Bernoulli distribution as the smallest neural network that doesn’t depend on input data. Although without practical value, this description pictures its main characteristics.

### Bernoulli Distribution and LogicPlum

LogicPlum’s platform uses the Bernoulli distribution in many areas. It is part of the set of discrete distributions considered by the platform, including the binomial distribution, the multinomial distribution, the geometric distribution, and more.

The great advantage of using this platform is efficiency, as it doesn’t require in-depth statistical knowledge from the user, and calculations are performed quickly.

###### Additional Resources

- Wikipedia.
*Bernoulli Distribution.*Available athttps://en.wikipedia.org/wiki/Bernoulli_distribution - The European Mathematical Society. (2001).
*Encyclopedia of Mathematics. Binomial Distribution.*Available athttps://encyclopediaofmath.org/index.php?title=Binomial_distribution