# The Uniform Distribution

The uniform distribution models a situation where a fixed number of outcomes all have an equal probability of occurring.

A uniform distribution has two parameters: the lower limit and the upper limit. The upper limit is exclusive, which means the highest possible value is actually one less than the upper limit.

Examples of the uniform distribution are:

Coin tossing when the coin is known to be unbiased has a uniform distribution with two possible values: 0 ('heads') and 1 ('tails'). The lower limit is 0. The upper limit is 2.

When rolling dice, the score has a uniform distribution with lower limit 1 and upper limit 7.

When choosing an element at random from a collection of

*n*elements, the (zero-based) index has a uniform distribution with lower limit 0 and upper limit*n*.

The discrete uniform distribution is implemented by the DiscreteUniformDistribution class. It has two constructors. The first constructor takes one argument: the upper limit of the distribution. This limit is exclusive. A sample from the distribution is always strictly smaller than the upper limit. The following constructs a discrete uniform distribution with samples in the range 0 to 4, inclusive:

`var uniform1 = new DiscreteUniformDistribution(5);`

The second constructor takes two arguments. The first argument is the lower limit for the distribution. The second parameter is the upper limit of the distribution. The following constructs a discrete uniform distribution for the number of eyes when rolling one dye:

`var uniform2 = new DiscreteUniformDistribution(1, 7);`

The DiscreteUniformDistribution class has two specific properties, LowerBound and UpperBound, which return the lower and upper limits of the distribution.

DiscreteUniformDistribution has one static (*Shared* in Visual Basic) method, Sample, which
generates a random sample using a user-supplied uniform random number generator. It has two overloads, corresponding
to each of the two constructors.

```
var random = new MersenneTwister();
int sample1 = DiscreteUniformDistribution.Sample(random, 4);
int sample2 = DiscreteUniformDistribution.Sample(random, 1, 7);
```

The above example uses the MersenneTwister class to generate uniform random numbers.

For details of the properties and methods common to all discrete probability distribution classes, see the topic on Discrete Distributions.