• Uniform means “remaining the same at all times“
• We see from the above graph that the height, $h$, remains the same over each uniform distribution.
• This is due to the fact that there is equal likelihood of each value, $x$, occurring
• This gives each distribution the shape of a rectangle.
• Because of this and the fact that the total area of any probability distribution must equal to 1:
  $(b-a) \times h = 1$ or, $h = \frac{1}{b-a}$
• This gives an area (or probability) between two $x$-values, $x_1$ and $x_2$:
  $P(x_1 \le x \le x_2) = (x_2 - x_1) \times \frac{1}{b-a} = \frac{x_2 - x_1}{b-a}$

The following metrics apply to uniform distributions:

• They have a lower limit (lowest possible value): min = $a$
• They have an upper limit (highest possible value): max = $b$
• The mean is: $\mu = \frac{a+b}{2}$
• The standard deviation is:  $\sigma = \frac{b-a}{\sqrt{12}}$
• The variance is: $\sigma^2 = \frac{(b-a)^2}{12}$
• The distribution is symmetric, so skewness = 0.

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