This is a question for mathematicians/statisticians. When finding the standard deviation for a uniform distribution, we are told to use the square root of ((b-a)^2 /12). My text book gives no explanation of the origin of the 12. Can anyone help me understand this?
In: Mathematics
Obviously 12 is 3*2^2, so that can be rewritten as (((b-a)/2)^2)/3, where (b-a)/2 is the radius of the interval [a,b]. Let’s call it r, so the formula is r^2/3, which is r^3/3r, or (r^3/3)/r that is the average value of the function x^2 on the interval [0,r], so it’s the average square of the distance of a random point from the mean of the distribution, i.e. variance.
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