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| The distribution is given by {{attachment:uniform.svg}} for any ''a ≤ x ≤ b''. | The distribution is given by {{attachment:uniform.svg}} for any ''a ≤ x ≤ b''. The function is defined for all real numbers so values of ''x'' outside that range map to 0. |
Uniform Distribution
The uniform distribution is a flat continuous probability distribution function. All values are equally likely.
Contents
Description
The distribution is given by 
for any a ≤ x ≤ b. The function is defined for all real numbers so values of x outside that range map to 0.
Moments
The expected value is given as E[X] = (a+b)/2. The derivation is:
Variance is given as Var[X] = (b-a)2/12. It is sometimes given as (a-b)2/12 instead, but it doesn't matter since the difference is squared and any sign is discarded.
The simplest derivation is through Var[X] = E[X2] - E[X]2. The second raw moment is calculated as:
Meanwhile the square of the expected value is simple to calculate:
Altogether now:
