Calculate PDF, CDF, mean and variance for the continuous uniform distribution on [a, b].
The continuous uniform distribution assigns equal probability density to all values in the interval [a, b]. It is the simplest continuous distribution and serves as a model for 'equally likely' outcomes over a range.
f(x) = 1/(b−a) for a ≤ x ≤ b, 0 otherwise
CDF
F(x) = (x−a)/(b−a) for a ≤ x ≤ b
Zero. For any continuous distribution, P(X = exact value) = 0. Probability only applies to intervals.
Random number generators, arrival times within a known window, and rounding errors are often modeled as uniform.