Uniform distribution (discrete)

The discrete uniform distribution is a statistical probability distribution ( uniform distribution ). A discrete random variable with a finite number of occurrences has a discrete uniform distribution when the probability for each of its manifestations is the same. It then applies.

Probability function

The probability function of the discrete uniform distribution is:

And thus it satisfies the distribution function

In the case gives the

The expected value is:

In the case of the discrete uniform distribution has the expected value ( using the Gaussian sum formula )

And variance

Typically, this probability distribution is applied to random experiments whose results are equally common. If one assumes (with or without justification) that the n elementary events are equally likely, it is called a Laplace experiment. Common examples of Laplace experiments are the Laplace - cube and the Laplace coin. See also Continuous uniform distribution, Laplace formula.


Six -sided Laplace cube

The random experiment is: A die is thrown once. The possible values ​​of the random variables are: . According to the classical view, the likelihood probability for each instance is the same. It then has the probability function

With the expected value for and:

And variance

Decision problem of Marketing

An application in practice could be about a problem of operations research ( marketing). A company wants to introduce a new product on the market

One tries to forecast the success of the product quantitatively. It is simplistic from 5 different quantities sold are assumed: 0, 1,000, 5,000, 10,000 and 50,000. Because of the likelihood of the individual sales figures no reliable estimate is possible using the simplicity equal probabilities.

It is now the decision-making process, that is, objectify the individual purchase decision, ie determine the expected average paragraph and think, about the basis of decision trees, the extent to which increased advertising spending could increase the sales figures.


The discrete uniform distribution is often also named after Pierre- Simon Laplace ( Laplace - cube). However, it has nothing to do with the continuous Laplace distribution.