Uniform Distribution

The Uniform Distribution is a probability mass function where all values have an equal chance of occurring.

Example

• Rolling a fair $6$ sided die
• Picking a marble that is any colour out of a bag with $2$ red, $2$ green and $2$ blue marbles
• Selecting any pizza slice at random from an evenly sliced pizza

Properties

The mean of the uniform distribution is simply the constant on which it is uniformly distributed. $\mu =x$

The variance of the uniform distribution for a can be calculated as:

Random Variable	Variance
Continuous Random Variable	$Var(x)=\frac{(b-a{)}^2}{12}$
Discrete Random Variable	$Var(x)=\frac{(b-a+1{)}^2-1}{12}$

Where

$a$ is the distribution’s minimum value $b$ is the distribution’s maximum value