## Uniform Distribution or Rectangular Distribution

Uniform distribution or rectangular distribution is a continuous probability distribution.

**Definition-**

A random variable X is said to follow uniform or rectangular distribution it follows the following probability distribution function.

And is denoted by X~U(a,b)

*Python Code to Plot Uniform Distribution*

**import numpy**

**import matplotlib.pyplot as plt**

**a=20**

**b=50**

**x= numpy.random.uniform(low=a,high=b,size=100)**

**plt.title(“Uniform Distribution(size=100)”)**

**plt.plot(x)**

**plt.savefig(“Uniform Distribution(size=100).png”)**

## And when size=5000 it becomes almost rectangular

**Mean for Uniform Distribution**

**Mean for Uniform Distribution**

## Variance for Uniform Distribution

## Applications of Uniform Distribution-

Uniform distribution is widely used by simulators.

- Monte Carlo simulator uses it in risk analysis.
- Network simulators use to set traffic generation parameters.

**Conclusion-**

Uniform probability distribution is a simple continuous probability distribution. Further, it helps to understand basics of probability distribution. If you want to learn probability distribution functions in statistics start from uniform distribution.