Discrete vs continuous

  • Discrete distributions (only specific values) have a probability mass function.
  • Continuous distributions (spectrum of values) have a probability density function.

Normal Distribution

The normal distribution is also known as the Gaussian distribution or Bell curve.

Binomial Distribution

The binomial distribution is a discrete distribution. It represents the number of successes in n independent experiments, each which have a yes/no values.

Its probability mass function is:

n is the number of trials. The PMF represnts the probability of getting k successes, when the probability of an individual success is p.

Bernoulli distribution

The Bernoulli distribution is a special case of the Binomial distribution in which n is 1; that is, it represents the probability of one yes/no experiment in which the possible outcomes are 0 and 1. For example, it can represent the probability of a single coin toss.

The two-point distribution is similar to the Bernoulli distribution, except for that the outcomes can be two other values, not necessarily just 0 and 1.

Sources