Statistics/Distributions/Uniform
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< Statistics  Distributions
Continuous Uniform Distribution[edit]
Probability density function Using maximum convention 

Cumulative distribution function 

Notation  

Parameters  
Support  
CDF  
Mean  
Median  
Mode  any value in 
Variance  
Skewness  0 
Ex. kurtosis  
Entropy  
MGF  
CF 
The (continuous) uniform distribution, as its name suggests, is a distribution with probability densities that are the same at each point in an interval. In casual terms, the uniform distribution shapes like a rectangle.
Mathematically speaking, the probability density function of the uniform distribution is defined as
And the cumulative distribution function is:
Mean[edit]
We derive the mean as follows.
As the uniform distribution is 0 everywhere but [a, b] we can restrict ourselves that interval
Variance[edit]
We use the following formula for the variance.