Bernoulli distribution

The Bernoulli distribution is the probability mass function that describes a discrete trial with two possible outcomes. We define the Bernoulli trial as:

$$p(0)=P(X=0)=1-p$$ $$p(1)=P(X=1)=p$$

$p$ is the parameter that the distribution follows.

$$X\sim \text{Bernoulli}(p)$$

The distributions below are for Bernoulli(0.5) and Bernoulli(0.8).¹

Calculations

The arithmetic mean:

$${\mu }_X=p$$

The population variance:

$${\sigma }_X^2=p(1-p)$$

See also

• Binomial distribution, a generalisation of the Bernoulli distribution

Footnotes

1. From Statistics for Engineers and Scientists by William Navidi. ↩