## Quantitative Methods

Discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair dice. The possible values are 1, 2, 3, 4, 5, 6, and each time the dice is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n). With these conventions, the cumulative distribution function of the discrete uniform distribution can be expressed,

There are a number of important types of discrete random variables. The simplest is the uniform distribution.

A random variable with p.d.f. (probability density function) given by:

P(X = x) = 1/(k+1) for all values of x = 0, ... k

P(X = x) = 0 for other values of x

where k is a constant, is said to be follow a uniform distribution.

#### Example

Suppose we throw a die. Let X be the random variable denoting what number is thrown.

P(X = 1) = 1/6

P(X = 2) = 1/6 etc

In fact, P(X = x) = 1/6 for all x between 1 and 6. Hence we have a uniform distribution.

#### Discrete Uniform Random Variable