Continuous uniform distribution

A probability distribution with constant density over a finite interval. Its probability for any subinterval is proportional to that subinterval’s length.

Probability density function: A function whose values describe probability per unit of a continuous variable, with total integral one. The distribution is defined by a density that stays constant across its interval.
Monte Carlo method: A computational method that uses repeated random sampling to estimate quantities. Uniform random numbers are a standard starting point for simulations.
Discrete uniform distribution: A probability distribution assigning equal probability to each value in a finite set. It is the discrete counterpart, assigning equal mass rather than constant density.
Continuous random variable: A random variable whose possible values range over a continuum and whose probabilities are described by a density. The distribution assigns probabilities to ranges, not positive mass to individual points.
Cumulative distribution function: A function giving the probability that a random variable is at most each specified value. For this distribution, cumulative probability increases linearly within the interval.
Random number generation: The production of numbers intended to behave like draws from a specified probability distribution. Many generators produce uniform values before transforming them into other distributions.
Normal distribution: A continuous distribution with a symmetric bell-shaped density determined by its mean and variance. Unlike the flat uniform density, its probability concentrates near the mean.
Probability measure: A mathematical rule assigning probabilities to events while satisfying the axioms of probability. The density specifies probabilities by integrating over measurable subsets of the interval.
Expected value: The probability-weighted average value of a random variable. Symmetry places the mean at the interval’s midpoint.
Rejection sampling: A method for sampling from a target density by accepting or rejecting proposals from an easier distribution. Uniform proposals can select vertical positions beneath a target density.

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