How this calculator works
All equal-width intervals within the support have equal probability. Density is the reciprocal of the support width, and cumulative probability increases linearly. Interval bounds outside the support contribute no extra probability. Equal endpoints are excluded because they describe a point mass rather than a continuous density.
Formula
f(x) = 1/(b-a) on [a,b]; F(x) = (x-a)/(b-a) within the support; E[X] = (a+b)/2; Var[X] = (b-a)²/12.
Worked example
For [2, 8], density is 1/6, mean is 5 and variance is 3. The interval [3, 5] contains probability 2/6 = 1/3.
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Frequently asked questions
Does every exact value have the same probability?
Every exact value has probability zero. Equal density means equal-width intervals have equal probability.
Are endpoints included?
Including or excluding a single endpoint makes no difference to continuous probability.
Can bounds be negative?
Yes, provided the maximum is greater than the minimum.