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

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)

In continuous probability distributions, P(X = k) = 0.

Example

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

Common errors

Uniform X = Uniform(5, 10); 
std::cout << X.P(11) << std::endl; //Error: Given value cannot be anything outside of [a, b].  

Good to know: k has to be within [a, b]