Category Archives: Teaching statistics

Univariate probability distributions

In probability and statistics, a probability distribution assigns a probability to every possible collection of outcomes of a random experiment. Examples are found in experiments whose sample space is non-numerical, where the distribution would be a categorical distribution; experiments whose sample space is encoded by discrete random variables, where the distribution is a probability mass function; and experiments with sample spaces encoded by continuous random variables, where the distribution is a probability density function.

A probability distribution can be specified in a number of different ways, each of which are equivalent, often chosen for mathematical convenience:

  1. by supplying a valid probability mass function or probability density function
  2. by supplying a valid cumulative distribution function or survival function
  3. by supplying a valid hazard function
  4. by supplying a valid characteristic function
  5. by supplying a rule for constructing a new random variable from other random variables whose joint probability distribution is known.

Important and commonly encountered probability distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution.

Introduction to the module

 

Probability distributions module