> For the complete documentation index, see [llms.txt](https://math-5.gitbook.io/math/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://math-5.gitbook.io/math/reference/statistics/uniform.md).
# Uniform
Assigns equal probability to all outcomes within a specified range. It is characterized by two parameters: 𝑎 (the minimum value of the range) and 𝑏 (the maximum value of the range)
## Create a new Uniform distribution
```cpp
Uniform X = Uniform(a, b);
```
creates a continuous Uniform probability distribution.
#### Distribution properties:
| Property | Type/Return type | Description |
|---|
a | double | Minimum value of the range. |
b | double | Maximum value of the range. |
E() | double | Returns the expected value of the range. |
D() | double | Represents variance, that measures the spread of dispersion of the random variable around its expected value E(X). |
P(int k) | double | The cumulative distribution function: P(X < k) |
{% hint style="info" %}
In continuous probability distributions, P(X = k) = 0.
{% endhint %}
## Example
{% tabs %}
{% tab title="Example of a uniform distribution" %}
//Example: for a range [2, 5], whats the probability of getting the number 3?
double a = 2; //min. of range
double b = 5; //max. of range
Uniform X = Uniform(a, b);
std::cout << X.P(3) << std::endl; //0.333333
{% endtab %}
{% tab title="Common errors" %}
```cpp
Uniform X = Uniform(5, 10);
std::cout << X.P(11) << std::endl; //Error: Given value cannot be anything outside of [a, b].
```
{% endtab %}
{% endtabs %}
{% hint style="info" %}
**Good to know:** *`k`* has to be within \[a, b]
{% endhint %}